Entropy and Temperature of Black 3-Branes

A.W. Peet (Princeton University); I.R. Klebanov; S.S. Gubser

REVIEW

Entropy and Temperature of Black 3-Branes

S.S. Gubser, I.R. Klebanov, A.W. Peet (Princeton University)

High Energy Physics - Theory · Submitted 25 Feb 1996 · 21 references

Pith's verdict: The scaling match between the black 3-brane horizon area and a 3+1 dimensional blackbody on the D3-brane is real and parameter-free; the coefficient mismatch is acknowledged up front, so the paper's actual claim is narrower than its reputation.

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arXiv IDhep-th/9602135 (version 3)

Pith IDO7XEIZYQ, Pith's permanent record of this paper and its review

CitationA.W. Peet (Princeton University), I.R. Klebanov, S.S. Gubser. "Entropy and Temperature of Black 3-Branes." arXiv:hep-th/9602135 (1996). https://pith.science/paper/O7XEIZYQ

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Editor's note

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Worth your time, and worth citing. The core result is that a slightly non-extremal black 3-brane has SBH scaling as (δM/M0)^{3/4}, and a 3+1 dimensional gas of massless open-string modes on the D3-brane gives the same exponent from E ~ VT^4, S ~ VT^3. Both sides are derived independently; nothing is fitted to get the exponent. That is the paper's real content, and it holds up. The second result is the boosted momentum-carrying 3-brane (Eq. 8): the extremal horizon area still vanishes even with finite ADM momentum, unlike the black string case, and this matches the non-extensivity of the BPS entropy. The general argument in Eq. 13 that s_BPS → 0 for any p > 1 is a clean observation I have not seen stated so compactly elsewhere. Credit where due: the supergravity algebra in Eqs. 27-31 is careful, and the ADM mass normalization is checked against the extremal mass formula rather than assumed. On the soft spots, I part company with the stress-test note on emphasis. The N = 6 versus N = 8 issue is real, but the authors raise it themselves in the abstract (abstract:s0, 'up to a mysterious factor') and again explicitly after Eq. 31, where they say plainly they do not understand it and float Tseytlin's periodic-gaugino suggestion as a guess. That is honest reporting of an open problem, not a hidden fit. Calling the paper near-circular overstates it: the exponent is not tuned, only the coefficient. The genuinely thin spots are smaller. Eq. 33's temperature relation is a restatement of the entropy relation, not an independent derivation from the metric, and the authors concede as much in Section 4. The 'marginal bound state' and confinement speculation at the end of Section 3 is loose talk and should be read as such. The claim that position-independent string coupling is necessary for agreement is asserted, not shown. For what it is worth, the (4/3)^{1/4} factor was later understood to be a weak-coupling artifact, which retroactively vindicates the authors' instinct to publish the mismatch rather than bury it. Who should read it: anyone working on brane thermodynamics or the black hole entropy program, and anyone who wants a clean worked example of matching a horizon area to a statistical count. Send it to referees.

Referee report

Significance

This is an early and influential entry in the D-brane counting of black-hole entropy, and its central scaling match is parameter-free: the (delta M/M0)^{3/4} exponent is obtained independently on the supergravity side (Eqs. 30-31) and on the gas side (Eqs. 22-26), not fitted. The paper deserves credit for reporting the numerical mismatch openly rather than suppressing it, and for stating the exact-agreement claim as a conjecture rather than a derivation. It also yields a falsifiable by-product, a Hawking temperature independent of the string coupling, which could in principle be checked against a string-amplitude computation of the decay rate, and it correctly isolates p = 1 as the case where the BPS entropy density is finite, sharpening the criterion for when D-brane counting should work.

Major objections (2)

[Section 3, Eq. (33)] The Hawking temperature is obtained by combining dM = T_H dS_BH with the gas relation dM = T dS, so Eq. (33) is a restatement of the entropy ratio S/S_BH = (N/6)^{1/4} rather than an independent derivation from the geometry. Since the abstract advertises the relation between the blackbody temperature and the Hawking temperature as a result, the paper should either compute T_H independently from the surface gravity of the metric (2) and show that it agrees, or state explicitly that Eq. (33) is a consistency check and carries no independent evidential weight. As written, a reader cannot tell whether the identification has support beyond the entropy relation it is derived from.
[Section 3, discussion following Eq. (31)] The exact coefficient agreement S = S_BH requires N = 6, whereas N = 4 super Yang-Mills gives N = 8; the paper is commendably explicit that this is a conjecture resting on Tseytlin's unpublished periodic-gaugino proposal (Ref. [18], private communication). The remaining unresolved question is what would test that proposal: the manuscript does not indicate any computation, such as a strong-coupling evaluation of the worldvolume free energy or a direct check of the gaugino boundary conditions, that could confirm or refute the reduction from 8 to 6 modes. Because the exact-agreement statement is the paper's most striking claim, a sentence on how it could be falsified would materially strengthen the discussion.

Minor objections (6)

[Section 2, Eq. (13)] The printed exponent (p+1)/(2p) is inconsistent with the sentence that immediately follows it. With S_BPS ~ n^{1/2} and n ~ L^{p+1}, the entropy density scales as s_BPS ~ L^{(1-p)/2}, which is finite for p = 1 and vanishes for p > 1, matching the paper's conclusion; the printed exponent instead gives s_BPS ~ L for p = 1, which contradicts the stated result. The exponent should be corrected to (1-p)/2.
[Section 3, Eq. (24)] The factor n_w in Eq. (24) should be n_w^{1/2}. Eliminating T from Eq. (23) gives S = (2/3) N^{1/4} sqrt(pi) n_w^{1/2} L^{3/4} E^{3/4}, and only with this power does the subsequent substitution of Eq. (25) reproduce the n_w^{5/4} of Eq. (26).
[Section 3, Eq. (32)] It would help to display the N-dependence of the ratio explicitly, S/S_BH = (N/6)^{1/4}, so that the reader can see at a glance that N = 6 is exactly the value that makes the two entropies coincide and that N = 8 gives (4/3)^{1/4}.
[Introduction] The statement that for p-branes with p < 3 'it is easy to check that the D-brane entropy is not proportional to the horizon area' is asserted without demonstration. A brief argument or a reference would make the criterion that the string coupling at the horizon must be controlled more convincing.
[Section 2, footnote 6] The observation that g_tt diverges on the horizon in the scaling limit qualifies the physical interpretation of the extremal momentum-carrying solution and deserves a sentence in the main text rather than only in a footnote.
[Section 3, Eq. (17)] The notation is slightly overloaded: k denotes the number of open strings in Eq. (17), while n_w denotes the number of coincident branes later in the section. A short clarifying sentence would prevent confusion.

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The paper

The paper claims

Black 3-brane entropy follows a hot open-string gas

The reading

The paper asks whether the horizon entropy of a black 3-brane in type IIB supergravity can be reproduced by counting microstates of the D3-brane that carries the same charge. For a slight departure from extremality, the supergravity entropy scales as $(/delta M/M_0)^{3/4}$, exactly the scaling of a $3+1$ dimensional gas of massless bosons and fermions, which is blackbody radiation. Counting the open-string modes on $n_w$ coincident D3-branes gives an entropy with the same power law and a normalization that matches the horizon-area result if the gas has six effective massless modes per brane rather than the eight expected from the worldvolume gauge theory. The paper also constructs a boosted 3-brane carrying longitudinal momentum and shows that its extremal horizon area still vanishes, consistent with the non-extensive BPS entropy on the D-brane side. If the identification is right, the horizon area is counting the states of a hot gas on the brane, and the Hawking temperature is the temperature of that gas.

What carries the argument

Two calculations carry the argument. On the gravity side, the horizon area of the type IIB 3-brane solution is expressed through the ADM mass and the deviation $/delta M/M_0$, giving $S_{/rm BH}/propto n_w^{5/4}L^3(/delta M/M_0)^{3/4}$. On the brane side, the grand-canonical partition function of a $3+1$ dimensional gas of $N$ massless bosons and fermions on a torus of side $L$ is $Z=/prod_{/vec n/in/mathbb{Z}^3}/left[(1+q^{|/vec n|})/(1-q^{|/vec n|})/right]^N$ with $q=e^{-2/pi/LT}$; it yields $E=/pi^2NL^3T^4/16$ and $S=/pi^2NL^3T^3/12$, so eliminating $T$ gives $S/propto N^{1/4}L^{3/4}E^{3/4}$. The boost of the 3-brane solution supplies the momentum-carrying case and lets the paper compare the extremal horizon area with the BPS entropy.

Extended reading notes

Core claim

The central claim is that a slightly non-extremal black 3-brane has a Bekenstein-Hawking entropy $S_{/rm BH}=2^{5/4}3^{-3/4}/pi^{7/8}n_w^{5/4}/kappa^{-3/4}L^3(/delta M/M_0)^{3/4}$ (Eq. 31) whose energy dependence matches the entropy $S=(2/3)N^{1/4}/sqrt{/pi}/,n_wL^{3/4}E^{3/4}$ (Eq. 24) of a $3+1$ dimensional gas of $N$ massless bosons and fermions on the D3-brane. With the expected $N=8$ the two entropies differ by the factor $(4/3)^{1/4}$; with $N=6$ they agree exactly. The paper calls the $N=8$ mismatch a mysterious numerical factor and does not derive the reduction to six, offering instead an unpublished suggestion about altered gaugino boundary conditions. It also shows that an extremal 3-brane carrying finite longitudinal momentum still has vanishing horizon area, matching the non-extensive BPS entropy of the momentum-carrying D3-brane.

Load-bearing premise

The argument rests on treating the non-BPS excitations of the D3-brane as a free $3+1$ dimensional gas of massless open-string modes and on reducing the expected eight massless modes to six so that the normalizations match, a reduction the paper itself leaves to an unpublished suggestion rather than deriving.

Editorial extensions

If this is right

If the matching is not accidental, the Bekenstein-Hawking entropy of a near-extremal D3-brane is the entropy of a $3+1$ dimensional blackbody gas of open strings, with the horizon area counting that gas's microstates.
The Hawking temperature is independent of the string coupling and equals the blackbody temperature when the effective mode count is $N=6$; for the expected $N=8$ it differs by the factor $(4/3)^{1/4}$.
For $n_w$ coincident D3-branes the gas has $n_w^2$ species, matching the enhanced symmetry of coincident branes.
An extremal 3-brane carrying finite longitudinal momentum still has zero horizon area, so unlike the black string, momentum does not stabilize a horizon for $p=3$; this agrees with the non-extensive BPS entropy on the D-brane side.

Reading between the lines

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

The scaling agreement is insensitive to the mode count, so the real test of the proposal is the coefficient: a first-principles finite-temperature computation of the D3-brane worldvolume theory should decide whether the effective light-mode count is six, eight, or something else.
If six is correct, it is an indirect clue about which worldvolume degrees of freedom survive at the temperatures where the supergravity description applies, possibly pointing to a topological or confining phase of the gauge theory rather than a free gas of all modes.
The $g$-independent Hawking temperature gives a concrete weak-coupling target: a string-amplitude calculation of the decay of an excited D3-brane should reproduce the same temperature and, if the identification is right, the same entropy coefficient.
Because the paper expects the comparison to fail for $p<3$ when the string coupling grows near the brane, mapping where the $p=3$ agreement breaks down would delineate the domain where horizon area is a reliable microstate counter.

Original abstract

We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane. These excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states. This is essentially the classic problem of blackbody radiation. The blackbody temperature is related to the temperature of the Hawking radiation. We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum. For extremal momentum-carrying 3-branes the horizon area vanishes. This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,526 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.84 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane. These excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states. This is essentially the classic problem of blackbody radiation. The blackbody temperature is related to the temperature of the Hawking radiation. We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum. For extremal momentum-carrying 3-branes the horizon area vanishes. This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane.	result 0.69	0.93	0.79	asserted 1.00
s1	These excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states.	method 0.80	0.45	0.06	asserted 1.00
s2	This is essentially the classic problem of blackbody radiation.	background 0.78	0.09	0.03	asserted 0.99
s3	The blackbody temperature is related to the temperature of the Hawking radiation.	interpretation 0.32	0.24	0.05	asserted 1.00
s4	We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum.	contribution 0.98	0.94	0.07	asserted 1.00
s5	For extremal momentum-carrying 3-branes the horizon area vanishes.	result 1.00	0.71	0.08	asserted 1.00
s6	This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity.	interpretation 0.89	0.40	0.11	asserted 0.60

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (21)

[18]

A. Tseytlin, private communication

View on Pith
[1]

J. Bekenstein, Lett. Nuov. Cim. 4 (1972) 737; Phys. Rev. D7 (1973) 2333; Phys. Rev. D9 (1974) 3292

View on Pith 1972
[2]

S.W. Hawking, Nature 248 (1974) 30; Comm. Math. Phys. 43 (1975) 199

View on Pith 1974
[3]

S.W. Hawking, Monthly Notices Roy. Astron. Soc. 152 (1971) 75; A. Salam, in Quantum Gravity: an Oxford Symposium (Eds. Isham, Penrose and Sciama, Oxford Univ. Press 1975); G. ’t Hooft, Nucl. Phys. B335 (1990) 138

View on Pith 1971
[4]

L. Susskind, Stanford preprint SU-ITP-94-33 (Septembe r 1994), hep-th/9309145; L. Susskind and J.R. Uglum, Phys. Rev. D50 (1994) 2700 [hep-th/9401070]; for a review, see L. Susskind and J.R. Uglum, Stanford prepri nt SU-ITP-95-31 (Novem- ber 1995), hep-th/9511227

View on Pith Pith review arXiv 1994
[5]

A. Sen, Mod. Phys. Lett. A10 (1995) 2081 [hep-th/9504147]

View on Pith Pith review arXiv 1995
[6]

J. Dai, R.G. Leigh, and J. Polchinski, Mod. Phys. Lett. A4 (1989) 2073; R.G. Leigh, Mod. Phys. Lett. A4 (1989) 2767

View on Pith 1989
[7]

J. Polchinski, Phys. Rev. Lett. 75 (1995) 4724 [hepth/9510017]

View on Pith 1995
[8]

A. Strominger and C. Vafa, Harvard and Santa Barbara prep rint HUTP-96-A002 (Jan- uary 1996), hep-th/9601029

View on Pith Pith review arXiv 1996
[9]

J.C. Breckenridge, R.C. Myers, A.W. Peet, and C. Vafa, Ha rvard and McGill and Prince- ton preprint HUTP-96/A005, McGill/96-07, PUPT-1592, hep- th/9602065. 9

View on Pith
[10]

C.G. Callan and J.M. Maldacena, Princeton preprint PUP T-1591 (February 1996), hep- th/9602043

View on Pith 1996
[11]

G.T. Horowitz and A. Strominger, Santa Barbara preprin t (February 1996), hep- th/9602051

View on Pith 1996
[12]

G.T. Horowitz and A. Strominger, Nucl. Phys. B360 (1991) 197

View on Pith 1991
[13]

J. Polchinski, S. Chaudhuri, and C.V. Johnson, Notes on D-Branes , Santa Barbara and ITP preprint NSF-ITP-96-003 (February 1996), hep-th/9602 052

View on Pith 1996
[14]

S.R. Das and S.D. Mathur, MIT and Tata preprint MIT-CTP- 2508 (January 1996), hep-th/9601152

View on Pith Pith review arXiv 1996
[15]

E. Witten, IAS preprint IASSNS-HEP-95-83 (October 199 5), hep-th/9510135

View on Pith Pith review arXiv
[16]

A. Tseytlin, Imperial preprint IMPERIAL-TP-95-96-26 (February 1996), hep- th/9602064

View on Pith 1996
[17]

M. Green and M. Gutperle, Cambridge preprint DAMTP-96- 12 (Feburary 1996), hep- th/9602077

View on Pith 1996
[19]

J.X. Lu, Phys. Lett. B313 (1993) 29, [hep-th/9304159]

View on Pith Pith review arXiv 1993
[20]

A similar mismatch in the entropy normalizations was al so found by A. Strominger, private communication

View on Pith
[21]

I.R. Klebanov and L. Thorlacius, Physics Letters B371 (1996) 51 (hep-th/9510200); S.S. Gubser, A. Hashimoto, I.R. Klebanov and J.M. Maldacena , Princeton preprint PUPT-1586 (January 1996), hep-th/9601057. 10

View on Pith Pith review arXiv 1996

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AC conductivities of the D3/D7 holographic Weyl semimetal show peaks and troughs near the WSM-insulator transition, traced to quasinormal-mode poles with small imaginary parts.
Heat and work in black hole thermodynamics via holography
hep-th 2024-12 conditional novelty 6.0 of 10

The paper derives first and second laws for composite black holes coupled through the boundary, with heat and work defined from boundary sources and bath energy flow.
Localized Black Holes in AdS$_3$: What Happens Below c/12 Stays Below c/12
hep-th 2024-12 conditional novelty 6.0 of 10

Localized black holes in AdS3 x S3 x T4 fill the low-energy spectrum, dominate the microcanonical ensemble below a small positive energy, and appear to have the same entanglement entropy as BTZ black holes.
Electroweak Phase Transition and Baryogenesis in Composite Higgs Models
hep-ph 2018-04 conditional novelty 6.0 of 10

When the Higgs and the dilaton roll together, the electroweak phase transition in composite Higgs models is naturally first-order, and varying charm mixings can generate enough CP violation for electroweak baryogenesi...
Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography
hep-ph 2014-12 conditional novelty 6.0 of 10

A bottom-up holographic model tuned to lattice QCD yields temperature-dependent second-order transport coefficients for the non-conformal quark-gluon plasma, packaged as fitting functions for hydrodynamic simulations.
Entwinement and the emergence of spacetime
hep-th 2014-06 conditional novelty 6.0 of 10

Entwinement, a symmetrized entanglement of gauged internal degrees of freedom, reconstructs the interior of a conical-defect AdS3 spacetime inside the region that ordinary spatial entanglement leaves dark.
A lattice study of the jet quenching parameter
hep-ph 2013-07 conditional novelty 6.0 of 10

Soft, non-perturbative contributions to the jet quenching parameter are large, and a lattice EQCD computation gives q-hat around 6 GeV squared per femtometer at T around 398 MeV.
5D super Yang-Mills theory and the correspondence to AdS$_7$/CFT$_6$
hep-th 2013-04 conditional novelty 6.0 of 10

5D super Yang-Mills on S5 reproduces the AdS7 supergravity Wilson loop at the symmetry-enlargement point, but the free energy agreement requires fitting the compactification radius to the free energy at a different hy...
Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma
hep-th 2011-06 conditional novelty 6.0 of 10

A regular finite-temperature supergravity solution dual to an anisotropic N=4 plasma yields a conserved stress tensor with a conformal anomaly and a phase diagram in which the homogeneous anisotropic phase can be unst...
From black holes to strange metals
hep-th 2010-03 conditional novelty 6.0 of 10

A charged black hole in anti-de Sitter space yields non-Fermi liquids whose low-energy behavior is controlled by an emergent one-dimensional conformal fixed point, reproducing strange-metal scaling including linear-in...
Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent
hep-th 2009-05 conditional novelty 6.0 of 10

Numerically constructed black holes in asymptotically Lifshitz spacetimes behave differently above and below z=2, with a continuous finite-energy family for z>2 and a temperature curve that develops negative slope bel...
Entropy production in collisions of gravitational shock waves and of heavy ions
hep-th 2008-05 conditional novelty 6.0 of 10

A trapped-surface calculation for colliding gravitational shock waves in anti-de Sitter space yields an entropy bound that matches RHIC heavy-ion data to roughly 10% at 200 GeV.
Mimicking the QCD equation of state with a dual black hole
hep-th 2008-04 conditional novelty 6.0 of 10

A five-dimensional black hole with a hand-tuned scalar potential reproduces the shape of the QCD equation of state, and a nonlinear master equation gives a general map from potential to equation of state.
Holographic Thermodynamics at Finite Baryon Density: Some Exact Results
hep-th 2007-09 accept novelty 6.0 of 10

Exact analytic D-brane solutions show that a supersymmetric gauge theory with massive flavor fields at finite baryon density has a second-order phase transition at chemical potential equal to the flavor mass.
Thermodynamics of the brane
hep-th 2007-01 conditional novelty 6.0 of 10

For probe D7 and D6 branes in black D3 and D4 backgrounds, the authors compute the fundamental matter's free energy, entropy, energy density and speed of sound, and find tachyonic brane modes exactly where the thermod...
Wilson loops in heavy ion collisions and their calculation in AdS/CFT
hep-ph 2006-12 accept novelty 6.0 of 10

The ratio of the jet quenching parameter in any two conformal theories with gravity duals equals the square root of the ratio of their central charges, motivating a QCD estimate about 0.63 times the N=4 SYM value.
Holographic phase transitions at finite baryon density
hep-th 2006-11 conditional novelty 6.0 of 10

At finite baryon density the holographic meson-melting transition persists as a line ending at a critical point, and a region of the resulting phase diagram becomes thermodynamically unstable.
Drag force in AdS/CFT
hep-th 2006-05 accept novelty 6.0 of 10

A classical string trailing behind a moving quark in an AdS5-Schwarzschild black hole yields the drag force dp/dt = -(pi sqrt(lambda)/2) T^2 v / sqrt(1 - v^2) in strongly coupled N=4 super-Yang-Mills plasma.
Holographic Phase Transitions with Fundamental Matter
hep-th 2006-05 accept novelty 6.0 of 10

The flavour-melting phase transition in holographic gauge theories is first order and universal across Dp/Dq probe-brane models, occurring above the gluon deconfinement temperature for heavy quarks.
Higher derivative corrections to near-extremal black holes in type IIB supergravity
hep-th 2006-04 conditional novelty 6.0 of 10

Leading alpha' corrections shift the Hawking-Page temperature by a factor of (1 - 40γ) and add a ln(T/ε) term to the free energy of charged black 3-branes with a chemical potential.
On Euclidean and Noetherian Entropies in AdS Space
hep-th 2006-04 conditional novelty 6.0 of 10

Euclidean and Wald entropy computations agree for higher-derivative corrected AdS5 Schwarzschild black holes, with a general Noether-charge argument explaining the equivalence.
Fivebranes from gauge theory
hep-th 2005-09 conditional novelty 6.0 of 10

The paper gives a unified construction of gravity duals for several sixteen-supercharge gauge theories and derives their near-BPS string spectra, including a (4,4) sigma model with non-central charges.
A universal result on central charges in the presence of double-trace deformations
hep-th 2002-12 conditional novelty 6.0 of 10

A double-trace deformation of a large-N CFT produces an infrared fixed point whose central charge differs from the ultraviolet one by a universal amount depending only on the operator dimension and spacetime dimension.
AdS/CFT and gravity
hep-th 1999-12 accept novelty 6.0 of 10

The Randall-Sundrum brane world is shown to be gravity coupled to a hidden conformal field theory, with radiation-dominated cosmology emerging on a slice of an AdS black hole and G4 = 2G5/L.
AdS/CFT Duals of Topological Black Holes and the Entropy of Zero-Energy States
hep-th 1999-06 conditional novelty 6.0 of 10

Hyperbolic AdS black holes carry entropy exceeding the weak-coupling gauge theory prediction at fixed energy, and the state isometric to pure AdS has 3/2 the free-field entropy with identical energy.
Phases of R-charged Black Holes, Spinning Branes and Strongly Coupled Gauge Theories
hep-th 1999-02 accept novelty 6.0 of 10

Charged black holes in anti-de Sitter space have an explicitly mapped phase diagram whose stability depends on whether charge or electric potential is held fixed, and they are equivalent to spinning D3-, M2-, and M5-branes.
Rotation and the AdS/CFT correspondence
hep-th 1998-11 conditional novelty 6.0 of 10

Rotating anti-de Sitter black holes and their dual conformal field theories both diverge at the critical angular velocity where the boundary rotates at the speed of light, and a new five-dimensional Kerr-AdS metric is...
A Correspondence Principle for Black Holes and Strings
hep-th 1996-12 conditional novelty 6.0 of 10

When a black hole's horizon curvature reaches the string scale, its Bekenstein-Hawking entropy matches the entropy of the strings and D-branes carrying the same charges, up to an order-one coefficient.
On the Underlying Nonrelativistic Nature of Relativistic Holography
hep-th 2025-02 conditional novelty 5.0 of 10

Standard AdS/CFT duality is reinterpreted as D-brane/black-brane duality in nonrelativistic D3-brane theory, with AdS5×S5 as a relativistic bubble in flat 3-Newton-Cartan geometry.
On the stability of holographic confinement with magnetic fluxes
hep-th 2024-11 conditional novelty 5.0 of 10

A bottom-up holographic model with magnetic flux on a circle shows a confining-to-conformal phase transition that occurs before a tachyonic instability, with the lightest scalar near the transition resembling a dilaton.

See all 84 Pith citations

How later papers used it

124 later papers cite it

Evidence: substantial. 121 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

Pith read 28 of the 145 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

3 later papers by other authors are listed below: 3 used its data or values.

Uses its data or values 3 of 10 papers with this label

Used this paper's pressure of the ideal Super-Yang-Mills plasma, P_0 = N_c^2 π^2 T^4/8, in its energy-momentum tensor for the near-quark region.

Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics (2009) · 0.90 · paraphrased: the licence does not allow quoting
Used this paper's result for N=4 SU(N) super-Yang-Mills, including a factor 3/4 due to strong coupling calculated from the AdS dual.

Electroweak Phase Transition and Baryogenesis in Composite Higgs Models (2018) · 0.97 · paraphrased: the licence does not allow quoting
Used this paper's result for N=4 SU(N) super-Yang-Mills to give the free energy in the approximately conformal, deconfined phase at χ=0.

High-Temperature Electroweak Baryogenesis with Composite Higgs (2023) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

121 arXiv papers cite this in 142 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 · 85 sentences without a confident label

Contests it 1 paper

Even though the framework proposed in [ref] can not be consistently implemented within a supergravity approximation of the string theory dual to $=4$ supersymmetric Yang-Mills (SYM) plasma in the Bjorken flow [ref] (see [ref] ), if correctly reproduces the equilibrium and near-equilibrium properties of the $=4$ SYM plasma obtained from the equilibrium correlation functions, , the equilibrium equation of state [ref] , its shear viscosity at infinite 't Hooft coupling [ref] , and its relaxation time[Related work appeared in [ref] .] [ref] .

Shear viscosity of boost invariant plasma at finite coupling · Introduction · contest 0.79

Builds on it 1 paper

Our picture provides a concrete path to the understanding of the rate of Hawking radiation for near-extremal asymptotically AdS$_5$ black holes from the dual $𝒩=4$ SYM, which generalizes the previous work by Callan and Maldacena [ref] for asymptotically flat black holes and the work by Gubser, Klebanov and Peet on near-extremal black D3-branes [ref] .

Toward an Effective CFT$_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation · Introduction · 1.00

Uses its method or tool 1 paper

In the large 't Hooft coupling limit, $λ_4 ≫1$, the entropy density can be calculated from the Bekenstein-Hawking entropy [ref] of non-extremal D3-branes with Ramond-Ramond charge (RR-charge) $N_c$, which is [ref] [equation] where $T$ is identified with the Hawking temperature of the black brane.

AdS/CFT aspects of the cosmological QCD phase transition · $𝒩 = 4$ SYM theory · 0.86

Uses its data or values 10 papers

The free energy are found to be $3/4$ of that in the zero coupling limit [ref] .

Thermodynamics of large-$N$ gauge theories on a sphere: weak versus strong coupling · Introduction · 0.95
The total energy-momentum tensor describing the near-quark region in the laboratory frame [for cylindrical coordinates $u^μ=(t,x_1,r,θ)$ quoted in dimensionless units, thus devided by $πT$] is determined to be [equation] where $P_0=N_c^2 π^2 T^4/8$ is the pressure of the ideal Super–Yang–Mills (SYM) plasma [ref] and $ξ=8√(λ) γ/N_c^2$.

Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics · Hard Probes in AdS/CFT · 0.90
In this case, the ratio is always a fixed constant which takes the value $ε/ε_0 = 0.75$ [ref] .

Quark Soup al dente: Applied Superstring Theory · The AdS/CFT Correspondence · 0.90

Compares with it 13 papers

This result agrees with [ref] and corresponds to the free energy of the $N = 4$ super Yang Mills at strong coupling.

On a Holographic Model for Confinement/Deconfinement · Confinement/deconfinement phase transition · 0.96
Of course, this is the same factor that appears in the usual AdS/CFT computations of the CFT at finite temperature [ref] .

Strongly Coupled Radiation from Moving Mirrors and Holography in the Karch-Randall model · Bootstrap Domain Wall Spacetimes · 0.86
This is analogous to the $43$ factor in a similar ratio of the thermal entropy [ref] (a similar ratio in $=1$ conformal field theories has been worked out recently in [ref] ).

Geometric Entropy and Hagedorn/Deconfinement Transition · Analysis of High Temperature Limit · 0.99

Cites it as background 30 papers

In more detail, the starting point for the classic derivation of AdS/CFT is the statement [ref] that [equation] and Maldacena's low-energy/near-horizon limit transmutes this equivalence into[Here we write AdS$_p+2×$S$^8-p$ as a metonym for the conformally-related [ref] near-horizon geometry of the RR black $p$-brane [ref] , Eq. ([ref]).

On the Underlying Nonrelativistic Nature of Relativistic Holography · Nonrelativity in Relativistic Holography · 0.92
Supergravity models provided a new way of understanding the unexpected “$3/4×$SB” entropy law [ref] that appears to explain numerical lattice QCD data above $T_c$ and the unexpected low viscosity of SQGP [ref] determined from collective elliptic flow data.

Conical Di-jet Correlations from a Chromo-Viscous Neck in AdS/CFT · Introduction · 0.82
The lessons learned from applying the AdS/CFT correspondence [ref] to the plasma phase of strongly coupled non-abelian gauge theories [ref] played a major role (see [ref] for a recent review).

Anomaly induced transport coefficients, from weak to strong coupling · Kubo Formulae and Holographic Triangle Anomalies · 0.90

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] [18]

A. Tseytlin, private communication

View on Pith

[2] [1]

J. Bekenstein, Lett. Nuov. Cim. 4 (1972) 737; Phys. Rev. D7 (1973) 2333; Phys. Rev. D9 (1974) 3292

View on Pith 1972

[3] [2]

S.W. Hawking, Nature 248 (1974) 30; Comm. Math. Phys. 43 (1975) 199

View on Pith 1974

[4] [3]

S.W. Hawking, Monthly Notices Roy. Astron. Soc. 152 (1971) 75; A. Salam, in Quantum Gravity: an Oxford Symposium (Eds. Isham, Penrose and Sciama, Oxford Univ. Press 1975); G. ’t Hooft, Nucl. Phys. B335 (1990) 138

View on Pith 1971

[5] [4]

L. Susskind, Stanford preprint SU-ITP-94-33 (Septembe r 1994), hep-th/9309145; L. Susskind and J.R. Uglum, Phys. Rev. D50 (1994) 2700 [hep-th/9401070]; for a review, see L. Susskind and J.R. Uglum, Stanford prepri nt SU-ITP-95-31 (Novem- ber 1995), hep-th/9511227

View on Pith Pith review arXiv 1994

[6] [5]

A. Sen, Mod. Phys. Lett. A10 (1995) 2081 [hep-th/9504147]

View on Pith Pith review arXiv 1995

[7] [6]

J. Dai, R.G. Leigh, and J. Polchinski, Mod. Phys. Lett. A4 (1989) 2073; R.G. Leigh, Mod. Phys. Lett. A4 (1989) 2767

View on Pith 1989

[8] [7]

J. Polchinski, Phys. Rev. Lett. 75 (1995) 4724 [hepth/9510017]

View on Pith 1995

[9] [8]

A. Strominger and C. Vafa, Harvard and Santa Barbara prep rint HUTP-96-A002 (Jan- uary 1996), hep-th/9601029

View on Pith Pith review arXiv 1996

[10] [9]

J.C. Breckenridge, R.C. Myers, A.W. Peet, and C. Vafa, Ha rvard and McGill and Prince- ton preprint HUTP-96/A005, McGill/96-07, PUPT-1592, hep- th/9602065. 9

View on Pith

[11] [10]

C.G. Callan and J.M. Maldacena, Princeton preprint PUP T-1591 (February 1996), hep- th/9602043

View on Pith 1996

[12] [11]

G.T. Horowitz and A. Strominger, Santa Barbara preprin t (February 1996), hep- th/9602051

View on Pith 1996

[13] [12]

G.T. Horowitz and A. Strominger, Nucl. Phys. B360 (1991) 197

View on Pith 1991

[14] [13]

J. Polchinski, S. Chaudhuri, and C.V. Johnson, Notes on D-Branes , Santa Barbara and ITP preprint NSF-ITP-96-003 (February 1996), hep-th/9602 052

View on Pith 1996

[15] [14]

S.R. Das and S.D. Mathur, MIT and Tata preprint MIT-CTP- 2508 (January 1996), hep-th/9601152

View on Pith Pith review arXiv 1996

[16] [15]

E. Witten, IAS preprint IASSNS-HEP-95-83 (October 199 5), hep-th/9510135

View on Pith Pith review arXiv

[17] [16]

A. Tseytlin, Imperial preprint IMPERIAL-TP-95-96-26 (February 1996), hep- th/9602064

View on Pith 1996

[18] [17]

M. Green and M. Gutperle, Cambridge preprint DAMTP-96- 12 (Feburary 1996), hep- th/9602077

View on Pith 1996

[19] [19]

J.X. Lu, Phys. Lett. B313 (1993) 29, [hep-th/9304159]

View on Pith Pith review arXiv 1993

[20] [20]

A similar mismatch in the entropy normalizations was al so found by A. Strominger, private communication

View on Pith

[21] [21]

I.R. Klebanov and L. Thorlacius, Physics Letters B371 (1996) 51 (hep-th/9510200); S.S. Gubser, A. Hashimoto, I.R. Klebanov and J.M. Maldacena , Princeton preprint PUPT-1586 (January 1996), hep-th/9601057. 10

View on Pith Pith review arXiv 1996