Minkowski-space correlators in AdS/CFT correspondence: recipe and applications

A.O.Starinets; D.T.Son

REVIEW

Minkowski-space correlators in AdS/CFT correspondence: recipe and applications

D.T.Son, A.O.Starinets

High Energy Physics - Theory · Submitted 7 May 2002 · 45 references

Pith's verdict: The paper that gave everyone a working recipe for real-time AdS/CFT; the derivation gap is real but the checks are honest and the conjecture is narrower than it looks.

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arXiv IDhep-th/0205051 (version 2)

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CitationA.O.Starinets, D.T.Son. "Minkowski-space correlators in AdS/CFT correspondence: recipe and applications." arXiv:hep-th/0205051 (2002). https://pith.science/paper/IQKJ2QYV

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Editor's note

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This is the paper that gave the field its working recipe for real-time correlators from gravity, and it is worth your time even though the central object is a conjecture. The prescription is one line: G_R = -2F(k,z)|_{z_B}, with f_k normalized to 1 at the boundary and incoming-wave at the horizon, and only the boundary term kept. What is new is that line, the two verification cases, the strong-coupling Chern-Simons rate, and the general argument that quasinormal frequencies are the poles of G_R. The last one is the cleanest thing in the paper and, I think, underrated: the argument in §4.3 that A(k)=0 in the near-boundary expansion is exactly the Dirichlet condition defining quasinormal modes is short, general, and correct. It reframes a numerical curiosity as a structural fact about linear response, and it holds beyond BTZ. The BTZ section is heavy but it is real work, and the matching to the 2d CFT Matsubara correlators at integer Δ (4.19, 4.22 against 4.34, 4.35) is a genuine independent check, not a consistency tautology. The zero-temperature dilaton check against the Wick-rotated Euclidean result is the other one. Both pass. The Chern-Simons rate (5.12) is a parameter-free prediction with no independent check at the time, and the paper says so by calling it a prediction rather than a result. That is the right posture. On the soft spots: the reader frames the weakest assumption as the discarded horizon term plus the boundary-condition identification. That is slightly off. For the incoming-wave solution the near-horizon phase makes f_{-k}∂_z f_k purely imaginary, so Re F(z_H)=0 and the real part of the prescription coincides with the real part of the on-shell action. The conjecture lives entirely in the imaginary part, where the prescription sets Im G_R to twice the horizon flux while the on-shell action gives zero by flux conservation. That is a sharper statement of the gap than the paper's own §3.2, and it is worth knowing. The stress-test note is right that the non-integer Δ BTZ result (4.16) is derived but never compared to the field-theory correlator (4.26), which is valid for any Δ. That comparison was available and was not made. It is a minor omission, not a hole, but it is the one place where the verification could have been tightened cheaply. The ǫ-dependent prefactors in (4.16)-(4.22) are divergent and dropped as contact terms; standard, but the bracket in (4.9) is carrying weight. Who should read it: anyone computing spectral functions, transport coefficients, or quasinormal modes in a holographic background. This is a foundational method paper and deserves a serious referee, with the expectation of revision on the derivation gap and the missing non-integer check.

Referee report

Significance

This is a foundational methods paper: it supplies the working recipe that made real-time AdS/CFT calculational practice possible, and the Chern-Simons rate (Eq. 5.12) is a genuine, falsifiable strong-coupling prediction with no weak-coupling counterpart available at the time. The two verification cases are chosen well and are non-trivial: the zero-temperature check reproduces the analytic continuation of the classic Euclidean result, and the BTZ check reproduces the field-theory Matsubara correlators computed independently from the Cardy formula. The quasinormal-mode/pole correspondence argument in §4.3 is a clean structural insight that has since become standard. The paper is candid about its scope: it states in §3.2 that the prescription 'does not follow strictly from an identity of the type (3.4)' and in §6 that it does not extend to higher-point functions. Those acknowledgements are appropriate and I do not treat them as newly discovered defects; the assessment below concerns what remains unstated or unchecked within the stated scope.

Major objections (3)

[§3.2, Eq. (3.15)] The manuscript would be substantially sharpened by stating explicitly where the conjecture actually resides. For the incoming-wave solution, f_{-k} ∂_z f_k at the horizon is purely imaginary (the near-horizon phase is a pure exponential and the derivative supplies a factor of i), so Re F(z_H) = 0 and the real part of (3.15) coincides with the real part of the on-shell action (3.13). The entire content of the conjecture is therefore the identification Im G_R = -2 Im F(z_H), i.e. twice the horizon flux, together with the factor of 2. Making this decomposition explicit would tell the reader precisely which two checks (the T=0 massless scalar and BTZ) are testing what, and would make the relation to the flux-conservation argument of §3.1 transparent rather than apparently in tension with it. This is a request to expose the logic, not a claim that the prescription is wrong.
[§4.2, Eqs. (4.16) and (4.26)] The finite-temperature verification is carried out only for integer conformal dimension and for T_L = T_R. The non-integer result (4.16) is derived but never compared to the field-theory correlator (4.26), which is valid for arbitrary Delta. Since the Fourier transform of (4.26) is the natural independent check and the machinery of §4.2 is already in place, extending the comparison to non-integer Delta (or stating why the integer case is the only one where the comparison is clean) would close the one gap in the finite-temperature validation. As it stands, the reader cannot tell whether (4.16) has been checked or merely written down.
[§5, Eqs. (5.10)-(5.12)] The Chern-Simons rate is presented as a prediction and cannot be tested independently, which the authors acknowledge. Because the numerical coefficient 1/(256 pi^3) is the paper's headline number, the normalization conventions that fix it should be stated explicitly rather than left to refs. [39,40]: the value of the constant K in (3.6) for the Ramond-Ramond scalar, and the normalization of O = (1/4) F F-tilde relative to the axion kinetic term. In addition, the term proportional to (1 - 1/u) in (5.10) diverges as u -> 0 and is dropped; the text should say explicitly that this is a contact term discarded under the prescription of §3.2, so that the reader can see the finite piece is what enters (5.11).

Minor objections (6)

[§4.1.2, Eq. (4.16)] The overall prefactor epsilon^{2 beta_+ - 2} is divergent for 1/2 < beta_+ < 1. This is presumably the standard cutoff-dependent normalization fixed by convention, as in (4.25), but the text should say so, and should note that neither the pole locations (4.23) nor the imaginary part (4.24) depend on this normalization.
[§4.3] The argument that zeros of A(k) produce poles of G_R is clean, but it implicitly assumes that the coefficients A(k) and B(k) in the near-boundary expansion are entire functions of omega. A sentence stating this assumption would make the argument airtight.
[§5, Eq. (5.7) and Eq. (5.10)] The hat notation is used inconsistently: (5.6) writes the dimensionless frequency and momentum as omega-hat_B and omega-hat_5, while (5.10) writes i omega-hat. Harmonizing the notation would help the reader follow the expansion.
[Appendix B, Eqs. (B.3)-(B.5)] The WKB estimate Im G_R ~ exp(-a|k|/T) with a ~ 0.835 is quoted without an explicit statement of its regime of validity in the main text. The conditions omega-hat >> 1 and s > 1 should be stated where the result is summarized, not only in the appendix.
[§3.1] The remark that the horizon term is 'commonly thought to be oscillating and hence averaged out to zero' would benefit from a citation to the discussions in refs. [5-9] where that view is expressed.
[General] The manuscript as supplied contains numerous broken inter-word spaces (e.g. 'Se attle', 'cons tant', 'fo rmulate'). These appear to be a production artifact rather than author errors, but a final pass before typesetting is advisable.

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The paper

The paper claims

A working recipe lets physicists compute real-time quantum correlators directly from a black hole's gravity dual, with the horizon's ingoing-wave condition standing in for the choice of retarded propagator.

The reading

Quantum field theories at finite temperature have several different real-time correlation functions — retarded, advanced, Feynman — and only the retarded one tells you how a system responds to a small push and how quickly it returns to equilibrium. The standard AdS/CFT dictionary was built in Euclidean signature, where there is only one correlator and analytic continuation back to real time requires knowing the answer at every Matsubara frequency, which gravity calculations almost never deliver. This paper proposes a direct Lorentzian recipe: solve the bulk wave equation for a field whose boundary value is fixed to one and which, at the horizon, is a purely ingoing wave; then read the retarded Green's function off the boundary term of the on-shell action, discarding the horizon term. The authors check the recipe against two cases where the answer is independently known — a massless scalar in pure anti-de Sitter space and the two-dimensional conformal theory dual to the BTZ black hole — and then apply it to predict a strong-coupling value for the Chern-Simons diffusion rate of hot $N=4$ super Yang-Mills.

What carries the argument

The load-bearing object is the boundary flux function $F(k,z) = K√{-g}g^{zz}f_{-k}(z)∂_zf_k(z)$, evaluated at the boundary only. Its imaginary part is radially conserved, so it can be computed at the horizon as a shortcut, but its real part at the boundary is what carries the correlator. The second piece of machinery is the horizon boundary condition: for timelike momenta the solution must be a purely ingoing wave (an outgoing wave for the advanced propagator), and for spacelike momenta it must be regular. The third piece is the observation that the normalisation coefficient $A(k)$ multiplying the non-normalisable branch vanishes precisely when the Dirichlet condition defining a quasinormal mode is imposed, which is why quasinormal frequencies appear as poles of $G_R$.

Extended reading notes

Core claim

The central claim is a prescription, not a theorem: for a bulk field $f_k(z)$ normalised to $1$ at the boundary and satisfying an ingoing-wave condition at the horizon, the retarded Green's function of the dual boundary operator is $G_R(k) = -2F(k,z)$ evaluated at the boundary, with $F(k,z) = K$ times $f_{-k}(z)$ times $f_k'(z)$ times the appropriate metric factor. The authors first explain why the naive Lorentzian version of the dictionary fails: differentiating the on-shell action gives a quantity whose imaginary part is a conserved flux, so the horizon contribution exactly cancels the boundary contribution and the result is real, whereas a retarded propagator must be complex. Their fix is to keep only the boundary term and to let the ingoing-wave condition at the horizon encode which real-time propagator is being computed. They verify the recipe at zero temperature, recovering $G_R(k) = N^2k^4/(64π^2)(ln|k^2| - iπθ(-k^2)sgn ω)$ for the operator dual to a massless scalar, and at finite temperature in the BTZ background, where the gravity result for the retarded correlator matches the analytic continuation of the known two-dimensional conformal field theory correlator. As an application they obtain a Chern-Simons diffusion rate $Γ = (g^2_{YM}N)^2 T^4/(256π^3)$ at large 't Hooft coupling, and they show that the poles of the retarded correlator are exactly the quasinormal frequencies of the black hole.

Load-bearing premise

The recipe assumes that discarding the horizon term of the on-shell action and keeping only the boundary term, combined with the ingoing-wave condition at the horizon, yields the retarded Green's function — a step the authors themselves say does not follow from any identity of the usual generating-functional form and justify only by the cases where an independent check exists.

Editorial extensions

If this is right

Real-time transport coefficients of strongly coupled gauge theories become computable from gravity without any Euclidean analytic continuation, starting with the Chern-Simons diffusion rate $Γ = (g^2_{YM}N)^2T^4/(256π^3)$.
The same machinery, applied to the graviton and to R-charge perturbations, yields the shear viscosity and charge diffusion rate of the thermal plasma, which the authors pursue in a companion paper.
The poles of the retarded Green's function coincide with black-hole quasinormal frequencies, giving a quantitative gravity-side account of how fast a perturbed strongly coupled plasma returns to thermal equilibrium.
The imaginary part of the correlator for spacelike momenta at high momentum is exponentially suppressed by a Boltzmann-like factor with a coefficient near $0.835$, which the authors note is stronger suppression than a weakly coupled plasma would give.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the recipe holds generally, it turns the quasinormal spectrum of any asymptotically anti-de Sitter black hole into a directly readable list of poles of a boundary correlator, which suggests quasinormal-mode numerics can be repurposed as a spectral calculator for strongly coupled matter.
The explicit failure of the naive on-shell-action route — a real answer where a complex one is required — suggests that Lorentzian holography needs a boundary-condition-dependent state-selection rule rather than a single generating functional, a point that a fully general formulation would have to absorb.
The gap between the strong-coupling diffusion coefficient scaling as $(g^2_{YM}N)^2$ and the weak-coupling $ (g^2_{YM}N)^5\ln(1/g^2_{YM}N)$ invites an interpolation question: whether a single monotonic function of the 't Hooft coupling connects the two regimes, which lattice or resummation work could in principle probe.

Original abstract

We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature N=4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature N=4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.

background contribution method result interpretation main claim

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence.	contribution 0.95	0.94	0.41	asserted 0.99
s1	This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole.	result 0.97	0.89	0.27	asserted 1.00
s2	Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature N=4 supersymmetric Yang-Mills theory in the strong coupling limit.	result 0.79	0.95	0.16	asserted 1.00
s3	We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.	interpretation 0.72	0.79	0.13	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from proof or derivation 0.97.

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References

Works cited (45)

[1]

J. Maldacena, The large N limit of superconformal ﬁeld theories and superg ravity, Adv. Theor. Math. Phys. 2 (1998) 231 [ hep-th/9711200]

View on Pith Pith review arXiv 1998
[2]

S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [ hep-th/9802109]

View on Pith Pith review arXiv 1998
[3]

E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150]

View on Pith Pith review arXiv 1998
[4]

G. Policastro and A. Starinets, On the absorption by near-extremal black branes, Nucl. Phys. B 610 (2001) 117 [ hep-th/0104065]

View on Pith Pith review arXiv 2001
[5]

V. Balasubramanian, P. Kraus, A. Lawrence and S.P. Trive di, Holographic probes of anti-de Sitter spacetimes, Phys. Rev. D 59 (1999) 104021 [ hep-th/9808017]

View on Pith Pith review arXiv 1999
[6]

V. Balasubramanian, S.B. Giddings and A. Lawrence, What do CFTs tell us about anti-de Sitter spacetimes?, J. High Energy Phys. 9903 (1999) 001 [ hep-th/9902052]

View on Pith Pith review arXiv 1999
[7]

V. Balasubramanian, P. Kraus and A. Lawrence, Bulk versus boundary dynamics in anti-de Sitter spacetime, Phys. Rev. D 59 (1999) 046003 [ hep-th/9805171]

View on Pith Pith review arXiv 1999
[8]

U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Vacua, propagators, and holographic probes in AdS/CFT, J. High Energy Phys. 9901 (1999) 002 [hep-th/9812007]

View on Pith Pith review arXiv 1999
[9]

S. Ryang, The Hadamard function and the Feynman propagator in the AdS/ CFT correspondence, Phys. Lett. B 469 (1999) 87 [ hep-th/9909186]

View on Pith Pith review arXiv 1999
[10]

G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, hep-th/0205052

View on Pith Pith review arXiv
[11]

M. Ba˜ nados, C. Teitelboim and J. Zanelli, Black hole in three-dimensional spacetime, Phys. Rev. Lett. 69 (1992) 1849 [ hep-th/9204099]

View on Pith Pith review arXiv 1992
[12]

M. Ba˜ nados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the 2+1 black hole, Phys. Rev. D 48 (1993) 1506 [ gr-qc/9302012]

View on Pith Pith review arXiv 1993
[13]

S.S. Gubser, Absorption of photons and fermions by black holes in four dim ensions, Phys. Rev. D 56 (1997) 7854 [ hep-th/9706100]

View on Pith Pith review arXiv 1997
[14]

J.L. Cardy, Conformal invariance and universality in ﬁnite size scalin g, J. Phys. A 17 (1984) L385. – 25 –

View on Pith 1984
[15]

A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, Moscow 1981. English translation: Integrals and Series. Vol. 1: Elementary Functions, Gordon & Breach Science Publishers, New York 1986

View on Pith 1981
[16]

V. P. Frolov and I. D. Novikov, Black hole physics: basic concepts and new developments, Kluwer Academic Publishers, Dordrecht 1998

View on Pith 1998
[17]

K. D. Kokkotas and B.G. Schmidt, Quasi-normal modes of stars and black holes, Living Rev. Rel. 2 (1999) 2 [ gr-qc/9909058]

View on Pith Pith review arXiv 1999
[18]

G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [ hep-th/9909056]

View on Pith Pith review arXiv 2000
[19]

S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS/CFT connection, Mod. Phys. Lett. A 14 (1999) 2635 [ hep-th/9905219]

View on Pith Pith review arXiv 1999
[20]

J.S.F. Chan and R.B. Mann, Scalar wave falloﬀ in asymptotically anti-de Sitter backgrounds, Phys. Rev. D 55 (1997) 7546 [ gr-qc/9612026]

View on Pith Pith review arXiv 1997
[21]

B. Wang, C.-Y. Lin and E. Abdalla, Quasinormal modes of Reissner-Nordstr¨ om anti-de Sitter black holes, Phys. Lett. B 481 (2000) 79 [ hep-th/0003295]

View on Pith Pith review arXiv 2000
[22]

V. Cardoso and J.P.S. Lemos, Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103]

View on Pith Pith review arXiv 2001
[23]

B. Wang, E. Abdalla and R.B. Mann, Scalar wave propagation in topological black hole backgrounds, Phys. Rev. D 65 (2002) 084006 [ hep-th/0107243]

View on Pith Pith review arXiv 2002
[24]

I.G. Moss and J.P. Norman, Gravitational quasinormal modes for anti-de Sitter black holes, Class. and Quant. Grav. 19 (2002) 2323 [ gr-qc/0201016]

View on Pith Pith review arXiv 2002
[25]

D. Birmingham, Choptuik scaling and quasinormal modes in the anti–de Sitte r space/conformal-ﬁeld theory correspondence, Phys. Rev. D 64 (2001) 064024 [hep-th/0101194]

View on Pith Pith review arXiv 2001
[26]

T.R. Govindarajan and V. Suneeta, Quasi-normal modes of AdS black holes: a superpotential approach, Class. and Quant. Grav. 18 (2001) 265 [ gr-qc/0007084]

View on Pith Pith review arXiv 2001
[27]

V. Cardoso and J.P.S. Lemos, Scalar, electromagnetic, and Weyl perturbations of BTZ black holes: Quasinormal modes, Phys. Rev. D 63 (2001) 124015 [ gr-qc/0101052]

View on Pith Pith review arXiv 2001
[28]

D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal ﬁeld theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [ hep-th/0112055]. – 26 –

View on Pith Pith review arXiv 2002
[29]

S.S. Gubser, I.R. Klebanov and A.W. Peet, Entropy and temperature of black 3-branes, Phys. Rev. D 54 (1996) 3915 [ hep-th/9602135]

View on Pith Pith review arXiv 1996
[30]

S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [ hep-th/9805156]

View on Pith Pith review arXiv 1998
[31]

V.A. Rubakov and M.E. Shaposhnikov, Electroweak baryon number non-conservation in the early universe and in high-energy collisions, Usp. Fi z. Nauk. 166 (1996) 493 [Phys. Usp. 39 (1996) 461] [ hep-ph/9603208]

View on Pith Pith review arXiv 1996
[32]

P. Arnold, D. Son and L.G. Yaﬀe, The hot baryon violation rate is O(α5wT 4), Phys. Rev. D 55 (1997) 6264 [ hep-ph/9609481]

View on Pith Pith review arXiv 1997
[33]

P. Huet and D.T. Son, Long range physics in a hot non-Abelian plasma, Phys. Lett. B 393 (1997) 94 [ hep-ph/9610259]

View on Pith Pith review arXiv 1997
[34]

D. B¨ odeker,Eﬀective dynamics of soft non-Abelian gauge ﬁelds at ﬁnite t emperature, Phys. Lett. B 426 (1998) 351 [ hep-ph/9801430]

View on Pith Pith review arXiv 1998
[35]

G.D. Moore, Do we understand the sphaleron rate?, hep-ph/0009161

View on Pith Pith review arXiv
[36]

C.R. Hu and B. M¨ uller, Classical lattice gauge ﬁeld with hard thermal loops, Phys. Lett. B 409 (1997) 377 [ hep-ph/9611292]

View on Pith Pith review arXiv 1997
[37]

G.D. Moore, C. Hu and B. M¨ uller, Chern-Simons number diﬀusion with hard thermal loops, Phys. Rev. D 58 (1998) 045001 [ hep-ph/9710436]

View on Pith Pith review arXiv 1998
[38]

G.D. Moore, The sphaleron rate: B¨ odeker’s leading log, Nucl. Phys. B 568 (2000) 367 [hep-ph/9810313]

View on Pith Pith review arXiv 2000
[39]

I.R. Klebanov, World-volume approach to absorption by non-dilatonic bran es, Nucl. Phys. B 496 (1997) 231 [ hep-th/9702076]

View on Pith Pith review arXiv 1997
[40]

S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, String theory and classical absorption by three-branes, Nucl. Phys. B 499 (1997) 217 [ hep-th/9703040]

View on Pith Pith review arXiv 1997
[41]

K. Heun, Zur Theorie der Riemann ’s sehen Functionen zweiter Ordnung mit vier Verzweigungspunkten, Math. Ann. 33 (1889) 61

View on Pith
[42]

Higher transcendental functions, vol. III , ed. A. Erdelyi, McGraw Hill, New York 1955

View on Pith 1955
[43]

Heun ’s diﬀerential equation, ed. A. Ronveaux, F. Arscott, Oxford University Press, Oxford 1995. – 27 –

View on Pith 1995
[44]

G. Policastro, D.T. Son and A.O. Starinets, Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066]

View on Pith Pith review arXiv 2001
[45]

F.W.J. Olver, Asymptotics and special functions , A K Peters, Wellesley 1997. – 28 –

View on Pith 1997

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Real-time holographic n-point functions are computed by gluing Lorentzian bulk segments to Euclidean caps along a chosen complex-time contour, with junction conditions that reproduce the correct time-ordered i-epsilon...
Building an AdS/CFT superconductor
hep-th 2008-03 accept novelty 8.0 of 10

A simple gravitational theory in anti-de Sitter space provides a holographic dual of a superconductor, with a second-order transition to a charged condensate, infinite DC conductivity, and a conductivity gap set by th...
Nonlinear Fluid Dynamics from Gravity
hep-th 2007-12 accept novelty 8.0 of 10

Einstein's equations in anti-de Sitter space, expanded in boundary derivatives, yield the nonlinear equations of a conformal fluid whose second-order transport coefficients are computed explicitly.
Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
hep-th 2006-05 accept novelty 8.0 of 10

A heavy quark moving through strongly coupled N=4 plasma loses momentum at a rate fixed by temperature and coupling alone, with a friction coefficient independent of the quark's mass.
Holography and hydrodynamics: diffusion on stretched horizons
hep-th 2003-09 accept novelty 8.0 of 10

Long-wavelength fluctuations of black-brane horizons obey fluid dynamics, and the derived shear-viscosity-to-entropy ratio equals 1/(4π) across the supergravity backgrounds checked.
Quasi-Normal Modes and thermalization in integrable Quantum Field Theories from the Thermodynamic Bethe Ansatz
hep-th 2026-11 conditional novelty 7.0 of 10

A modified Thermodynamic Bethe Ansatz is conjectured to compute thermal damping and oscillation frequencies in integrable quantum field theories directly from scattering data.
Exact thermal correlators at vanishing momenta and the black hole singularity
hep-th 2026-11 accept novelty 7.0 of 10

Exact zero-momentum thermal three-point functions in holographic CFTs are derived and shown to contain the proper time to the black hole singularity in subleading exponential terms.
Holographic two-point functions across a PT symmetry-breaking transition
hep-th 2026-10 accept novelty 7.0 of 10

By deforming the holographic dipole model, the authors obtain two-point functions that interpolate between power-law, logarithmic, and log-oscillatory behavior across an exceptional point.
Love at First Loop: Quantum Deformability of Near-Extremal Black Holes
hep-th 2026-10 accept novelty 7.0 of 10

Quantum effects from the Schwarzian mode produce non-zero static Love numbers for near-extremal Reissner-Nordström black holes for ℓ≥1, with running and threshold behavior.
Metric and dilaton information from high-overtone quasinormal modes of analytic Einstein-Maxwell-dilaton black holes
hep-th 2026-10 accept novelty 7.0 of 10

A neutral scalar probe with a dilaton-dependent mass profile allows high-overtone quasinormal-mode spectra to separately determine the metric exponents and the signed dilaton exponent of an Einstein–Maxwell–dilaton bl...
Coherent Release Fronts in Krylov Chains and Thermal AdS$_2$ Response
hep-th 2026-10 accept novelty 7.0 of 10

An exact moving-cut occupation profile for a finite Krylov sector coupled to a conformal tail is derived, its derivative equals the squared filtered emission amplitude, and the shallow parameters are matched to a ther...
Strongly Coupled Soft Functions
hep-ph 2026-08 conditional novelty 7.0 of 10

The cusp anomalous dimension at strong coupling is obtained for all rapidity separations from two competing string saddles, and the transversely-separated two-cusp Wilson loop scales as (b_perp^2 Lambda^2)^{-Re Gamma_cusp}.
Light-like retarded correlators and the horizon
hep-th 2026-07 accept novelty 7.0 of 10

At large light-like momenta, holographic retarded correlators scale as a horizon-curvature-dependent power of ω, weaker than the naive ω^{2Δ−d}.
Selecting Complex Extremal Surfaces with the Kontsevich--Segal--Witten Criterion
hep-th 2026-07 conditional novelty 7.0 of 10

In AdS3, dS3, and AdS4 hyperbolic examples, the Kontsevich-Segal-Witten criterion uniquely selects a three-piece complex contour for timelike extremal surfaces, while timelike strips in AdS4 violate the criterion near...
Anti-scrambling and euclidean folds from observer correlators in de Sitter space
hep-th 2026-07 conditional novelty 7.0 of 10

Semiclassical gravity in de Sitter space produces four-point observer correlators whose sign of the scrambling correction is opposite to the black-hole case (anti-scrambling); the authors propose bounded-energy quantu...
A Lindbladian for holographic Brownian motion
hep-th 2026-06 unverdicted novelty 7.0 of 10

Derives and analyzes a Lindbladian for holographic Brownian motion in BTZ and AdS5 black brane backgrounds from the influence functional.
Analytic approaches to perturbations of strongly coupled Yang-Mills plasma
hep-th 2026-06 unverdicted novelty 7.0 of 10

Seiberg-Witten instanton expansions combined with exact WKB period integrals allow analytic computation and continuation of quasinormal modes from large q to q=0.
Bouncing singularities and thermal correlators on line defects
hep-th 2026-03 unverdicted novelty 7.0 of 10

Retarded correlators of displacement operators on line defects in holographic thermal CFTs exhibit bouncing singularities that match between interior-sensitive WKB and boundary-only OPE analyses.
Bulk-cone singularities and echoes from AdS exotic compact objects
hep-th 2025-12 unverdicted novelty 7.0 of 10

AdS exotic compact objects imprint bulk-cone singularities from null geodesics and echoes from trapped waves on CFT Green functions, signaling no horizon.
The Effects of Near-AdS$_2$ Backreaction on Matter Fields
hep-th 2025-09 conditional novelty 7.0 of 10

Backreaction of near-AdS2 geometry gives a temperature correction to scalar correlators that for massive fields needs metric backreaction, matches BTZ, and corrects the standard prescription.
Thermal Correlators and Black Holes: From Infinity to Singularity
hep-th 2025-08 conditional novelty 7.0 of 10

The stress-tensor part of thermal correlators develops complex-time singularities at exactly the locations where bulk geodesics reflect off the black hole singularity, and in Gauss-Bonnet holography ANEC saturation ma...
Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun
hep-th 2024-12 conditional novelty 7.0 of 10

An analytic low-temperature expression for the retarded Green's function of a charged scalar in the RN-AdS5 black brane is derived from the Heun connection problem, with QNM and superconductor applications verified nu...
Rigorous bounds on transport from causality
hep-th 2022-12 accept novelty 7.0 of 10

Causality implies that any dissipative dispersion relation has a finite radius of convergence and yields two-sided bounds on all transport coefficients, including an upper bound on diffusivity.
Cauchy Slice Holography: A New AdS/CFT Dictionary
hep-th 2022-04 conditional novelty 7.0 of 10

A T^2-deformed CFT partition function on a bulk Cauchy slice is proposed to equal a Wheeler-DeWitt wavefunction, giving an explicit map between bulk canonical quantum gravity states and boundary CFT states.
Pole skipping away from maximal chaos
hep-th 2020-10 conditional novelty 7.0 of 10

Pole skipping in the thermal energy density correlator is set by the stress tensor contribution to chaos, (ω,p) = i(2π/β)(1, 1/u_B^(T)), verified exactly in the large-q SYK chain at all couplings.
Black hole scrambling from hydrodynamics
hep-th 2017-10 conditional novelty 7.0 of 10

The holographic butterfly effect, normally extracted from gravitational shock waves, is shown to be encoded in a hydrodynamic sound mode at imaginary momentum, with the Lyapunov exponent and butterfly velocity emergin...
Deriving covariant holographic entanglement
hep-th 2016-07 conditional novelty 7.0 of 10

Running the replica trick on a real-time Schwinger-Keldysh contour and lifting it into the bulk, the authors show the saddle-point geometry forces the replica fixed-point surface to be extremal, which is the covariant...
Constructing higher-order hydrodynamics: The third order
hep-th 2015-07 accept novelty 7.0 of 10

The complete third-order gradient expansion of the relativistic fluid stress-energy tensor is classified, giving 20 conformal and 68 non-conformal transport coefficients, five combinations of which are computed hologr...
Metal-insulator transition in holography
hep-th 2012-12 conditional novelty 7.0 of 10

A holographic model with a homogeneous helical lattice exhibits a quantum phase transition between a metal with a Drude peak and an insulator with a soft gap, reproducing qualitative features of real correlated-electr...
Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
hep-th 2011-09 accept novelty 7.0 of 10

The retarded propagators of scalars and gravitons in the de Sitter static patch are controlled by a hidden SL(2,R) x SL(2,R) symmetry inherited from a conformally related AdS3, and can be reproduced by a level-matched...
Holographic Gravitational Anomaly and Chiral Vortical Effect
hep-th 2011-07 conditional novelty 7.0 of 10

A holographic model with a mixed gauge-gravitational Chern-Simons term yields the same T-squared chiral vortical conductivity as free chiral fermions, suggesting the coefficient is not renormalized.
Non-universal shear viscosity from Einstein gravity
hep-th 2010-11 conditional novelty 7.0 of 10

In a holographic p-wave superfluid with backreaction, the helicity-one shear viscosity η_xy deviates from the universal η/s = 1/4π below the critical temperature while the helicity-two η_yz remains universal.
Towards strange metallic holography
hep-th 2009-12 accept novelty 7.0 of 10

Probe D-branes in a Lifshitz background give resistivity proportional to T^(2/z) divided by charge density, so a dynamical exponent z=2 reproduces the linear resistivity of strange metals.
Quantum oscillations and black hole ringing
hep-th 2009-08 conditional novelty 7.0 of 10

Charged fermions in a holographic black hole background generate de Haas-van Alphen oscillations in the magnetic susceptibility at one loop, with power-law rather than delta-function nonanalyticities.
Spectral sum rules for the quark-gluon plasma
hep-ph 2009-03 accept novelty 7.0 of 10

Two exact shear-channel sum rules and a corrected bulk-channel sum rule are derived for N=4 SYM and pure Yang-Mills, with the N=4 shear rules verified numerically to four to five digits.
Real-time gauge/gravity duality: Prescription, Renormalization and Examples
hep-th 2008-12 conditional novelty 7.0 of 10

Real-time correlators in a holographic background follow from gluing Lorentzian and Euclidean bulk segments along the field theory's time contour, with radial counterterms unchanged and i-epsilon factors fixed by the ...
Hot Spacetimes for Cold Atoms
hep-th 2008-07 accept novelty 7.0 of 10

Black hole solutions with Schrödinger asymptotics are constructed in type IIB supergravity, and their dual non-relativistic CFTs are shown to have shear viscosity saturating the KSS bound eta/s = 1/4pi.
AdS/CFT duality for non-relativistic field theory
hep-th 2008-06 conditional novelty 7.0 of 10

Non-relativistic conformal field theories in d-1 spatial dimensions are proposed to be dual to gravity in AdS_{d+2} with a compact null circle, with Schrödinger symmetry emerging from boundary conditions on bulk fields.
The gravity dual of a p-wave superconductor
hep-th 2008-05 accept novelty 7.0 of 10

A charged black hole with a vector condensate in AdS4 realizes a p-wave superconductor whose conductivity is anisotropic, and whose p+ip cousin is unstable toward the pure p-wave state.
Local Fluid Dynamical Entropy from Gravity
hep-th 2008-03 accept novelty 7.0 of 10

The event horizon of gravity duals to fluid flows is located order by order in a derivative expansion, and its area form pulls back to a boundary entropy current with non-negative divergence guaranteed by the area theorem.
Impure AdS/CFT
hep-th 2008-01 conditional novelty 7.0 of 10

In a holographic strongly coupled fluid, impurity-induced momentum relaxation is suppressed by magnetic field and charge density for one operator, but diverges near sqrt(B^2 + rho^2/sigma_0^2) = 21 T^2 for the other, ...
Relativistic viscous hydrodynamics, conformal invariance, and holography
hep-th 2007-12 accept novelty 7.0 of 10

Conformal symmetry fixes five second-order transport coefficients in viscous hydrodynamics, and holography plus a Bjorken-flow match determine three of them for strongly coupled N=4 super Yang-Mills.
Viscosity Bound Violation in Higher Derivative Gravity
hep-th 2007-12 accept novelty 7.0 of 10

In Gauss-Bonnet gravity duals the shear viscosity to entropy density ratio is (1/4π)(1-4λ_GB), which drops below the conjectured 1/4π bound for positive coupling.
Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
hep-th 2007-12 accept novelty 7.0 of 10

General R^2 corrections to AdS gravity shift the dual theory's viscosity-to-entropy ratio by a term proportional to c3, and in the N=2 Sp(N) theory with fundamental and antisymmetric matter this pushes the ratio below 1/(4π).
Quantum critical transport, duality, and M-theory
hep-th 2007-01 accept novelty 7.0 of 10

The N=8 SU(N) superconformal Yang-Mills theory in 2+1 dimensions obeys an exact relation K_L K_T = N^3/(18 pi^2) between longitudinal and transverse current correlators at all frequencies and momenta, derived from the...
Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory
hep-th 2004-06 conditional novelty 7.0 of 10

The shear viscosity to entropy ratio of N=4 supersymmetric Yang-Mills plasma is (1/4π)(1 + (135/8) ζ(3) (g²N_c)^{-3/2} + ...), a positive correction that keeps the ratio above the conjectured 1/4π bound.
Schwinger-Keldysh Propagators from AdS/CFT Correspondence
hep-th 2002-12 conditional novelty 7.0 of 10

A gravity prescription using Kruskal coordinates and horizon boundary conditions reproduces the full 2x2 Schwinger-Keldysh propagator of a finite-temperature field theory from its AdS black-hole dual.
From AdS/CFT correspondence to hydrodynamics. II. Sound waves
hep-th 2002-10 accept novelty 7.0 of 10

Gravity dual of a hot N=4 SYM plasma reproduces the hydrodynamic sound-wave pole, including the speed of sound 1/sqrt(3) and the attenuation coefficient q^2/(6 pi T).
From AdS/CFT correspondence to hydrodynamics
hep-th 2002-05 accept novelty 7.0 of 10

Using the AdS/CFT duality, the authors derive the R-charge diffusion constant and shear viscosity of strongly coupled N=4 super Yang-Mills plasma from real-time correlation functions, showing hydrodynamic behavior eme...
Spectral function, OPE, and QNMs detect different singular points of black branes with unequal R-charges
hep-th 2026-11 accept novelty 6.0 of 10

Spectral function, OPE coefficients, and QNM lines in STU black branes are each dominated by different singular points behind the horizon, forming a right triangle of optical times.
A signature of the timelike singularity in holography
hep-th 2026-10 accept novelty 6.0 of 10

For a charged AdS5 black brane, the vacuum-subtracted spectral density has a predicted exponentially small tail governed by the complex time of a null geodesic reflecting off the timelike singularity, with a universal...
U(1) Current Diffusion in Gauss-Bonnet Holography
hep-th 2026-10 conditional novelty 6.0 of 10

All-order holographic U(1) transport in a Gauss-Bonnet brane shifts the electric and magnetic conductivities and the frequency dependence of the diffusion function, while leaving the leading diffusion constant unchang...
Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes
gr-qc 2026-10 conditional novelty 6.0 of 10

An explicit, mode-independent matrix transformation separates the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes into radial and angular systems valid at all complex frequencies.
Thermal properties of the $\rho$ meson from a machine-learning-improved holographic QCD model
hep-ph 2026-10 conditional novelty 6.0 of 10

A lattice-calibrated soft-wall holographic model predicts rho-meson melting near T = 168 MeV and a transition from a Breit-Wigner peak to a transport-dominated spectral function.

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How later papers used it

589 later papers cite it

Evidence: substantial. 576 of the citing papers share no author with it, and 290 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 1,110 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

21 later papers by other authors are listed below: 21 used its method or tool.

Uses its method or tool 21 of 284 papers with this label

Used the prescription first set out in this paper to compute two-point retarded Green's functions and the electrical conductivity via Kubo's formula.

Transport Coefficients of Black MQGP M3-Branes (2014) · 1.00 · paraphrased: the licence does not allow quoting
Used the holographic recipe for calculating retarded Green's functions from this paper with the Green-Kubo formula to find the shear viscosity to entropy ratio.

The shear viscosity of the non-commutative plasma (2007) · 1.00 · paraphrased: the licence does not allow quoting
Applied the real-time recipe of this paper to obtain the retarded Green's function.

Transport Coefficients at Zero Temperature from Extremal Black Holes (2009) · 1.00 · paraphrased: the licence does not allow quoting
Followed the prescription of this paper for calculating the shear viscosity.

Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling (2008) · 1.00 · paraphrased: the licence does not allow quoting
We bring the on-shell gravity action into the following form S^on-shell_reg = V_2∫dω/2πϕ^(0)_ωF(ω,u)|_u=ϵ^u=1ϕ^(0)_ω,and then according to the recipe [ref] , the retarded Green's function is G_R(ω) = -2lim_ϵ→0F(ω,ϵ),In the following, we compute the action terms up quadratic terms in perturbations.

Holographic Hydrodynamics of {\it Tilted} Dirac Materials (2022) · Holographic retarded Green's function and reduced $η/s$ · 1.00
Used the gauge/gravity dual prescription of this paper for calculating Green functions in Minkowski spacetime.

Isospin diffusion in thermal AdS/CFT with flavor (2007) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper for the Green's function, expanding near z=0.

Spatial scalar correlator in strongly coupled hot N=4 Yang-Mills theory (2010) · 1.00 · paraphrased: the licence does not allow quoting
Used the prescription in this paper to obtain the retarded Green's function for the holographic system and evaluate the sum rule integration.

Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas (2010) · 1.00 · paraphrased: the licence does not allow quoting
Extracted the Minkowski correlator of this paper from the boundary action using the procedure explained.

Negative Refraction and Superconductivity (2011) · 1.00 · paraphrased: the licence does not allow quoting
We hence showed that we can systematically find the charge of the scalar field in the NH region and then employ the retarded Green's function method by [ref] in order to determine the QNM frequencies.

Bosonic und Fermionic Quasinormal Modes of Rotating Black Holes Through AdS/CFT (2022) · Kerr-Solution · 1.00
Followed the prescription of this paper to calculate the glueball retarded Green's function.

Black-hole quasinormal modes and scalar glueballs in a finite-temperature AdS/QCD model (2009) · 1.00 · paraphrased: the licence does not allow quoting
Computed real time correlators following the recipe of this paper in the Schwarzschild-like patch of the black hole.

Real time response on dS_3: the Topological AdS Black Hole and the Bubble (2009) · 1.00 · paraphrased: the licence does not allow quoting
Followed this paper for the prescription to calculate Minkowskian correlators in AdS/CFT correspondence.

On Aspects of Holographic Thermal QCD at Finite Coupling (2015) · 1.00 · paraphrased: the licence does not allow quoting
Applied the Minkowski AdS/CFT prescription of this paper to compute the correlation function.

Relaxation time of a CFT plasma at finite coupling (2008) · 1.00 · paraphrased: the licence does not allow quoting
Used the prescription of this paper for obtaining the retarded Green function to arrive at the two-point retarded Green function of the U(1) baryon charge current.

Hydrodynamics and transport coefficients in an infrared-deformed soft-wall AdS/QCD model at finite temperature (2013) · 0.99 · paraphrased: the licence does not allow quoting
Applied the Lorentzian AdS/CFT prescription of this paper to obtain the transverse component needed for the photoemission rate computation.

Plasma photoemission from string theory (2012) · 0.95 · paraphrased: the licence does not allow quoting
Used the expansion coefficients of the retarded correlators of this paper in spatial momentum to determine the refractive index.

Refractive index in generalized superconductors with Born-Infeld electrodynamics (2018) · 0.94 · paraphrased: the licence does not allow quoting
From this connection formulae we read out the source and the response function for the bulk field and using the holographic prescription [ref] we obtain the retarded Green's function for the scalar primary operators in the 4-dimensional thermal $CFT$.

Exact thermal correlators of holographic $CFT$s (2022) · Conclusion · 0.98
Used the usual AdS/CFT prescription of this paper, evaluating at the asymptotic boundary with infalling boundary conditions at the horizon, to find the retarded Green's function.

Transport Properties of Holographic Defects (2008) · 0.99 · paraphrased: the licence does not allow quoting
Used the correct prescription of this paper for computing the retarded polarization tensor.

Light-like mesons and deep inelastic scattering in finite-temperature AdS/CFT with flavor (2009) · 0.95 · paraphrased: the licence does not allow quoting
Regarded the ratio of the response to the source as the retarded Green's function of this paper, imposing ingoing boundary conditions on the horizon.

Holographic Thermal Correlators for Hyperbolic $CFT$s (2023) · 0.89 · paraphrased: the licence does not allow quoting

How the literature uses it

561 arXiv papers cite this in 1,079 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 516 sentences without a confident label

Contests it 2 papers

In fact since both $g(r_+)$ and $h_t x_1(r_+)$ vanish there is only a contribution from the horizon from the last term, but this vanishes after integrating over all $ω$ (this is in contrast to statements made in [ref] ).

Conformal field theories in $d=4$ with a helical twist · Derivatives of the on-shell action and the relationship to the Green's function · contest 0.88
The original prescription of [ref] correctly but a-priori unjustifiably ignores the horizon contribution to the on-shell action.

All order effective action for charge diffusion from Schwinger-Keldysh holography · Son-Starinets prescription for retarded correlators revisited · contest 0.75

Builds on it 2 papers

The usual prescription proposed in [ref] to obtain the Green's function is generalized in the present setup as follows.

Holographic Operator Mixing and Quasinormal Modes on the Brane · Holographic Green's functions · 0.93
Finally, a generalization of the prescription of [ref] to the case of multiple fluctuation fields results in the above formula for the retarded Green function.

S-Wave Superconductivity in Anisotropic Holographic Insulators · Holographic Renormalization and Operator Mixing · 0.96

Uses its method or tool 273 papers

Further, we move on to the computation of two-point retarded Green's functions by using the prescription first set out in [ref] using which one can calculate the electrical conductivity by utilising Kubo's formula.

Transport Coefficients of Black MQGP M3-Branes · Introduction · 1.00
Using the holographic recipe for calculating retarded Greens functions [ref] and the Green-Kubo formula [ref] we find η_1 = lim_ω→0 1/ω (-2 F(u=0)) = N^2 πT^3/8 , which leads to the universal value $η/s = 1/ 4π$ for the shear viscosity to entropy ratio.

The shear viscosity of the non-commutative plasma · Scalar channel. · 1.00
The prescription for computing the retarded Green's function [ref] is that we solve the equation for our scalar field in the black hole background ([ref]) with ingoing boundary conditions at the black hole horizon $z=1$, ψ∼(1-z)^i / (h^2 +q^2-3) .

Impure AdS/CFT · Numerical results for $1/τ_imp$ · 1.00

Uses its data or values 2 papers

The absorption of the axions by the black hole with a cross section equal to the area of the black hole delivers the following result [ref] : Γ= (g^2 N)^2/256 π^3 T^4 , showing that topological transitions become more frequent at strong coupling, even though the dependence on the coupling is weaker than suggested by Eq.[ref].

Topology, magnetic field, and strongly interacting matter · Chern-Simons diffusion in non-Abelian plasma at strong coupling: holography · 0.82
In QCD at high temperature, the chirality flipping rate is estimated from the sphaleron rate as $Γ_sphal∼α_s^5 T^4$ [ref] , where $α_s$ is the strong coupling constant.

Foundations and Applications of Quantum Kinetic Theory · Recursive relation and semi-classical expansion in equilibrium and constant fields · 0.86

Compares with it 17 papers

Our quadratic influence functional results computed using a natural extension of the recently proposed holographic SK prescription of [ref] match with the long known results of [ref] under following coordinate transformations and redefinition of parameters

Open effective theory of scalar field in rotating plasma · Quadratic effective theory · 0.98
This result agrees with [ref] and obeys the KSS bound [ref] .

Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale · Scalar Mode and Shear Viscosity · 0.93
It clearly shows that the timelike extra dimension can effect the two-points correlation functions both in massless and massive fields when comparing with the normal Minkowski space [ref] .

New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity · two-points correlation functions · 1.00

Cites it as support 3 papers

We thus expect $G^R_χ$ to have no singularity at $k,ω= 0$, an assertion also backed by the AdS/CFT correspondence [ref] .

Energy and momentum dependence of the soft-axion interaction rate · Update on axion contribution to $ΔN^ _eff$ · 1.00
An example which motivates such a conjecture is the relation between the poles of retarded two-point functions of the dual quantum theory at the boundary, which determine the properties of return to equilibrium, and quasinormal modes of AAdS black holes [ref] .

Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach · Obstructions to the inversion of Rehren duality · 0.98
There are many examples in QCD [ref] and holography [ref] where this is confirmed.[In those examples the operator in the correlator was the stress tensor $T$ in four dimensions rather than $ϕ$.

Thermal CFTs in momentum space · Sum rules · 0.98

Cites it as background 104 papers

Having reviewed the construction in [ref] of the delocalized type IIA mirror of the type IIB background of [ref] as well its M-theory uplift, in 2.5, we will briefly review the general gauge-gravity duality techniques of [ref] of obtaining two-point functions involving energy momentum tensor/currents and summarize a host of results of [ref] obtained as a result of its application.

On Aspects of Holographic Thermal QCD at Finite Coupling · Type IIB and M-Theory Thermodynamics · 0.88
The real-time formulation of holography initiated in [ref] (see also [ref] ) relates the Fourier space retarded Green's functions $G^R(ω,k)$ of boundary operators to the solutions of classical bulk equations for perturbations obeying ingoing boundary conditions at the black hole horizon.

Horizon constraints on holographic Green's functions · Introduction · 0.93
In particular, thermodynamic and hydrodynamic behavior are encoded in black hole geometries and their quasi-normal modes (QNMs) [ref] .

Holographic D-brane constructions with dynamical gauge fields · Introduction · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

J. Maldacena, The large N limit of superconformal ﬁeld theories and superg ravity, Adv. Theor. Math. Phys. 2 (1998) 231 [ hep-th/9711200]

View on Pith Pith review arXiv 1998

[2] [2]

S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [ hep-th/9802109]

View on Pith Pith review arXiv 1998

[3] [3]

E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150]

View on Pith Pith review arXiv 1998

[4] [4]

G. Policastro and A. Starinets, On the absorption by near-extremal black branes, Nucl. Phys. B 610 (2001) 117 [ hep-th/0104065]

View on Pith Pith review arXiv 2001

[5] [5]

V. Balasubramanian, P. Kraus, A. Lawrence and S.P. Trive di, Holographic probes of anti-de Sitter spacetimes, Phys. Rev. D 59 (1999) 104021 [ hep-th/9808017]

View on Pith Pith review arXiv 1999

[6] [6]

V. Balasubramanian, S.B. Giddings and A. Lawrence, What do CFTs tell us about anti-de Sitter spacetimes?, J. High Energy Phys. 9903 (1999) 001 [ hep-th/9902052]

View on Pith Pith review arXiv 1999

[7] [7]

V. Balasubramanian, P. Kraus and A. Lawrence, Bulk versus boundary dynamics in anti-de Sitter spacetime, Phys. Rev. D 59 (1999) 046003 [ hep-th/9805171]

View on Pith Pith review arXiv 1999

[8] [8]

U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Vacua, propagators, and holographic probes in AdS/CFT, J. High Energy Phys. 9901 (1999) 002 [hep-th/9812007]

View on Pith Pith review arXiv 1999

[9] [9]

S. Ryang, The Hadamard function and the Feynman propagator in the AdS/ CFT correspondence, Phys. Lett. B 469 (1999) 87 [ hep-th/9909186]

View on Pith Pith review arXiv 1999

[10] [10]

G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, hep-th/0205052

View on Pith Pith review arXiv

[11] [11]

M. Ba˜ nados, C. Teitelboim and J. Zanelli, Black hole in three-dimensional spacetime, Phys. Rev. Lett. 69 (1992) 1849 [ hep-th/9204099]

View on Pith Pith review arXiv 1992

[12] [12]

M. Ba˜ nados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the 2+1 black hole, Phys. Rev. D 48 (1993) 1506 [ gr-qc/9302012]

View on Pith Pith review arXiv 1993

[13] [13]

S.S. Gubser, Absorption of photons and fermions by black holes in four dim ensions, Phys. Rev. D 56 (1997) 7854 [ hep-th/9706100]

View on Pith Pith review arXiv 1997

[14] [14]

J.L. Cardy, Conformal invariance and universality in ﬁnite size scalin g, J. Phys. A 17 (1984) L385. – 25 –

View on Pith 1984

[15] [15]

A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, Moscow 1981. English translation: Integrals and Series. Vol. 1: Elementary Functions, Gordon & Breach Science Publishers, New York 1986

View on Pith 1981

[16] [16]

V. P. Frolov and I. D. Novikov, Black hole physics: basic concepts and new developments, Kluwer Academic Publishers, Dordrecht 1998

View on Pith 1998

[17] [17]

K. D. Kokkotas and B.G. Schmidt, Quasi-normal modes of stars and black holes, Living Rev. Rel. 2 (1999) 2 [ gr-qc/9909058]

View on Pith Pith review arXiv 1999

[18] [18]

G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [ hep-th/9909056]

View on Pith Pith review arXiv 2000

[19] [19]

S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS/CFT connection, Mod. Phys. Lett. A 14 (1999) 2635 [ hep-th/9905219]

View on Pith Pith review arXiv 1999

[20] [20]

J.S.F. Chan and R.B. Mann, Scalar wave falloﬀ in asymptotically anti-de Sitter backgrounds, Phys. Rev. D 55 (1997) 7546 [ gr-qc/9612026]

View on Pith Pith review arXiv 1997

[21] [21]

B. Wang, C.-Y. Lin and E. Abdalla, Quasinormal modes of Reissner-Nordstr¨ om anti-de Sitter black holes, Phys. Lett. B 481 (2000) 79 [ hep-th/0003295]

View on Pith Pith review arXiv 2000

[22] [22]

V. Cardoso and J.P.S. Lemos, Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103]

View on Pith Pith review arXiv 2001

[23] [23]

B. Wang, E. Abdalla and R.B. Mann, Scalar wave propagation in topological black hole backgrounds, Phys. Rev. D 65 (2002) 084006 [ hep-th/0107243]

View on Pith Pith review arXiv 2002

[24] [24]

I.G. Moss and J.P. Norman, Gravitational quasinormal modes for anti-de Sitter black holes, Class. and Quant. Grav. 19 (2002) 2323 [ gr-qc/0201016]

View on Pith Pith review arXiv 2002

[25] [25]

D. Birmingham, Choptuik scaling and quasinormal modes in the anti–de Sitte r space/conformal-ﬁeld theory correspondence, Phys. Rev. D 64 (2001) 064024 [hep-th/0101194]

View on Pith Pith review arXiv 2001

[26] [26]

T.R. Govindarajan and V. Suneeta, Quasi-normal modes of AdS black holes: a superpotential approach, Class. and Quant. Grav. 18 (2001) 265 [ gr-qc/0007084]

View on Pith Pith review arXiv 2001

[27] [27]

V. Cardoso and J.P.S. Lemos, Scalar, electromagnetic, and Weyl perturbations of BTZ black holes: Quasinormal modes, Phys. Rev. D 63 (2001) 124015 [ gr-qc/0101052]

View on Pith Pith review arXiv 2001

[28] [28]

D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal ﬁeld theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [ hep-th/0112055]. – 26 –

View on Pith Pith review arXiv 2002

[29] [29]

S.S. Gubser, I.R. Klebanov and A.W. Peet, Entropy and temperature of black 3-branes, Phys. Rev. D 54 (1996) 3915 [ hep-th/9602135]

View on Pith Pith review arXiv 1996

[30] [30]

S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [ hep-th/9805156]

View on Pith Pith review arXiv 1998

[31] [31]

V.A. Rubakov and M.E. Shaposhnikov, Electroweak baryon number non-conservation in the early universe and in high-energy collisions, Usp. Fi z. Nauk. 166 (1996) 493 [Phys. Usp. 39 (1996) 461] [ hep-ph/9603208]

View on Pith Pith review arXiv 1996

[32] [32]

P. Arnold, D. Son and L.G. Yaﬀe, The hot baryon violation rate is O(α5wT 4), Phys. Rev. D 55 (1997) 6264 [ hep-ph/9609481]

View on Pith Pith review arXiv 1997

[33] [33]

P. Huet and D.T. Son, Long range physics in a hot non-Abelian plasma, Phys. Lett. B 393 (1997) 94 [ hep-ph/9610259]

View on Pith Pith review arXiv 1997

[34] [34]

D. B¨ odeker,Eﬀective dynamics of soft non-Abelian gauge ﬁelds at ﬁnite t emperature, Phys. Lett. B 426 (1998) 351 [ hep-ph/9801430]

View on Pith Pith review arXiv 1998

[35] [35]

G.D. Moore, Do we understand the sphaleron rate?, hep-ph/0009161

View on Pith Pith review arXiv

[36] [36]

C.R. Hu and B. M¨ uller, Classical lattice gauge ﬁeld with hard thermal loops, Phys. Lett. B 409 (1997) 377 [ hep-ph/9611292]

View on Pith Pith review arXiv 1997

[37] [37]

G.D. Moore, C. Hu and B. M¨ uller, Chern-Simons number diﬀusion with hard thermal loops, Phys. Rev. D 58 (1998) 045001 [ hep-ph/9710436]

View on Pith Pith review arXiv 1998

[38] [38]

G.D. Moore, The sphaleron rate: B¨ odeker’s leading log, Nucl. Phys. B 568 (2000) 367 [hep-ph/9810313]

View on Pith Pith review arXiv 2000

[39] [39]

I.R. Klebanov, World-volume approach to absorption by non-dilatonic bran es, Nucl. Phys. B 496 (1997) 231 [ hep-th/9702076]

View on Pith Pith review arXiv 1997

[40] [40]

S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, String theory and classical absorption by three-branes, Nucl. Phys. B 499 (1997) 217 [ hep-th/9703040]

View on Pith Pith review arXiv 1997

[41] [41]

K. Heun, Zur Theorie der Riemann ’s sehen Functionen zweiter Ordnung mit vier Verzweigungspunkten, Math. Ann. 33 (1889) 61

View on Pith

[42] [42]

Higher transcendental functions, vol. III , ed. A. Erdelyi, McGraw Hill, New York 1955

View on Pith 1955

[43] [43]

Heun ’s diﬀerential equation, ed. A. Ronveaux, F. Arscott, Oxford University Press, Oxford 1995. – 27 –

View on Pith 1995

[44] [44]

G. Policastro, D.T. Son and A.O. Starinets, Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066]

View on Pith Pith review arXiv 2001

[45] [45]

F.W.J. Olver, Asymptotics and special functions , A K Peters, Wellesley 1997. – 28 –

View on Pith 1997