Correlation functions for M^N/S_N orbifolds

Oleg Lunin; Samir D. Mathur

REVIEW

Correlation functions for M^N/S_N orbifolds

Oleg Lunin, Samir D. Mathur

High Energy Physics - Theory · Submitted 25 Jun 2000 · 21 references

Pith's verdict: A practical, mostly self-checking method for twist correlators in S_N orbifolds, with the general 3-point formula in hand but only the one- and two-overlap cases usable in closed form.

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arXiv IDhep-th/0006196 (version 3)

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CitationOleg Lunin, Samir D. Mathur. "Correlation functions for M^N/S_N orbifolds." arXiv:hep-th/0006196 (2000). https://pith.science/paper/4LNSU3TM

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Editor's note

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The thing to know: Lunin and Mathur give a working recipe for twist-operator correlators in M^N/S_N, and the recipe itself is the contribution. Replace the twisted path integral on the sphere by a path integral on the cover with no operator insertions, pay a Liouville factor that depends only on c, and you get every correlator as a sum over a finite range of genera. That reframing is clean and it is what makes the rest possible. The explicit genus-zero 3-point coefficient (eq. 6.19) is new, and the genus-one 4-point example (eq. 7.49) reproduces the old Z2 result of Dixon-Friedan-Martinec-Shenker, which is a real check rather than a decoration. The WZW fusion-rule analogy and the 1/N suppression of higher genus are structural consequences of the combinatorics, not fitted claims, and the stringy-exclusion remark at the end follows from the same counting. I would not oversell it beyond the D1-D5/orbifold crowd, but within that crowd it is the paper you want on the shelf next to Jevicki-Mihailescu-Ramgoolam, which only handled the extremal (one-overlap) case by recursion. This one covers the non-extremal cases too, at least in principle. On the reader's flagged weak point: I think that pick is wrong. The identity insertion at the punctures is not a heuristic — the lowest-dimension twist operator is the twisted-sector ground state, which on the cover is the vacuum, and the cylinder argument at eq. 3.22 makes the dimension count explicit. The stress-test note is right that this concern does not land. The genuine soft spots are smaller. Eq. 6.19 is opaque for general d2; the usable results are the one-overlap (6.21) and two-overlap (6.24) special cases, and the claimed full symmetry in n, m, q is asserted via a symbolic check that is not shipped. That is a minor reproducibility gap, partly covered by the factorization limits in 7.27, 7.30, 7.33. The 4-point section openly declines to sum the branches (7.2), and the supersymmetric extension is deferred to elsewhere; both are stated, not hidden. Who should read it: anyone computing orbifold CFT correlators for AdS3/CFT2, or anyone who needs the fusion coefficients rather than just the dimensions. Send it to referees. The method is sound, the checks are real, and the gaps are the kind a referee can pin down in a report rather than the kind that sink the claim.

Referee report

Significance

This is a foundational method paper for symmetric orbifold CFTs, which are central to the D1-D5 system and AdS3/CFT2. The covering-space technique is practical and widely applicable, and the genus-zero results are parameter-free in the sense that they depend only on the central charge. The explicit three-point coefficients and the genus-one four-point check against the Z2 orbifold computation of Dixon et al. are substantial results. The paper also provides several independent consistency checks: regularization parameters cancel in the OPE coefficients (Eqs. 6.15-6.18), the four-point function factorizes correctly in the w -> 0, w -> 1, and w -> infinity limits (Eqs. 7.27, 7.30, 7.33), and the genus-one result (Eq. 7.49) agrees with the published Z2 computation. The WZW fusion-rule analogy and the stringy-exclusion observation are interesting and clearly framed as observations rather than derivations.

Minor objections (5)

[Section 2.3] The identification of the lowest-dimension twist operator with a multiple of the identity operator on the covering surface is introduced with the phrase 'The answer is of course...' and justified by a slowest-power-law falloff heuristic. The later cylinder argument in Eq. (3.22) supplies the missing rationale; a forward reference there would make the logic explicit and reassure readers that the identity insertion is not merely a heuristic.
[Eq. (6.19)] The symmetry of the genus-zero three-point coefficient in n, m, and q is stated to have been checked by symbolic manipulation, but neither the code nor an analytic argument is provided. Since this symmetry is a nontrivial check on the result, a short appendix or a few lines explaining how the discriminant expression (5.25) rearranges under permutations would strengthen the paper.
[Section 6.3, Eq. (6.31)] The combinatorial prefactor for the normalized operators O_n is dense. A brief derivation of the factor N!/(N-s)! and the centralizer factors would help readers reproduce the large-N scaling N^{-(g+1/2)} and connect Eq. (6.31) to the earlier definition (6.26).
[Section 8.3, Figure 1] The plot of R(n; N) would benefit from a caption defining the axes and stating explicitly that the curve is for N = 1000. The current text refers to 'the figure' without specifying the normalization of the vertical axis.
[Section 7.4] The comparison with Dixon et al. is a strong check on the genus-one calculation. It would be helpful to state explicitly which equation in Ref. [9] corresponds to the noncompact boson case and which to the compact boson case, so that readers can verify the agreement without consulting the reference.

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The paper

The paper claims

Twist correlators in a symmetric orbifold collapse to a single covering surface, and the sphere term depends only on the central charge.

The reading

The paper asks how to compute correlation functions of twist operators — the fields that cyclically permute copies of a target space — in the two-dimensional conformal field theory whose target is the symmetric orbifold $M^N/S_N$. These theories are the proposed low-energy description of the D1–D5 brane system, so their correlators are the conformal-field-theory side of an AdS$_3$/CFT$_2$ duality, yet the nonabelian permutation group had blocked the techniques developed for cyclic orbifolds. The authors replace the path integral with twist insertions by a path integral on a covering Riemann surface carrying no operator insertions at all, then weight it by a Liouville action that depends only on the central charge $c$ of a single copy of $M$. If the construction holds, every twist correlator becomes a finite sum over genera of ordinary partition functions, the sphere term is the same for every choice of $M$, and the genus of the cover organizes itself into a $1/N$ expansion.

What carries the argument

The load-bearing device is the covering map. For three twist operators of orders $n,m,q$ placed at $0,a,$, the cover is written as a ratio of two polynomials $z=f_1(t)/f_2(t)$ whose Wronskian is forced by the local branching to take the form $f_2^2,dz/dt = C,t^{n-1}(1-t)^{m-1}$; this turns the search into a hypergeometric equation, solved explicitly in terms of Jacobi polynomials. The Liouville field $= [|dz/dt|^2]$ is then harmonic outside the punctures, so the conformal anomaly integral collapses to a sum of boundary contributions, one for each branch point and each image of infinity. A discriminant of Jacobi polynomials handles the product over the images of infinity. This is what makes the method work where stress-tensor Ward identities would not: no explicit stress tensor is needed, and the fusion coefficients follow from two- and three-point functions alone rather than from factorizing a four-point function.

Extended reading notes

Core claim

The central claim is that for $S_N$ orbifolds the correlator of twist operators equals $e^{S_L}Z(1/2)/(Z_$), where $S_L$ is a Liouville action computed purely from the local behaviour of the covering map at its punctures. Because the Liouville field $= _t$ is harmonic away from isolated points, $S_L$ reduces to boundary integrals around those punctures, and the answer depends on the target only through $c$. From this the authors extract closed-form genus-zero three-point couplings (their eq. 6.19), with simplified expressions for the single-overlap case $q=m+n-1$ and the two-overlap case $q=m+n-3$, and check that the general expression is symmetric in all three orders. They then compute a four-point function $$, finding a genus-zero contribution whose operator-product limits reproduce the three-point couplings, and a genus-one contribution for $^4$ that agrees with the known $Z_2$ orbifold result. Two structural consequences are drawn: a genus-$g$ cover is suppressed by $N^{-(g+1/2)}$, so the sphere term dominates at large $N$; and the condition for a nonzero genus-zero three-point function mimics the $SU(2)$ Wess–Zumino–Witten fusion rules with spins $j=(n-1)/2$ and level $k=N-1$, so that $j_1+j_2+j_3 k$. The authors also observe that the three-point coupling falls below its large-$N$ value once the twist orders approach $N$, which they read as a manifestation of the stringy exclusion principle.

Load-bearing premise

The construction assumes that the lowest-dimension twist operator corresponds to inserting a multiple of the identity operator at each puncture of the covering surface, a choice justified in the paper only by the heuristic that it gives the slowest power-law falloff of the partition function at large separation.

Editorial extensions

If this is right

Any twist correlator in $M^N/S_N$ is a finite sum over genera of partition functions of a single copy of $M$, so the sphere term is fixed by the central charge alone and is identical for $T^4$, $K3$, or a free boson.
The genus of the covering surface supplies a $1/N$ expansion with the term of genus $g$ suppressed by $N^{-(g+1/2)}$, giving a systematic large-$N$ organizing principle for the dual string theory.
Genus-zero three-point couplings vanish unless the twist orders obey an $SU(2)$-like triangle and truncation rule with $j=(n-1)/2$ and $k=N-1$, matching the pattern of Wess–Zumino–Witten fusion.
The three-point coupling drops relative to its large-$N$ limit once twist orders reach order $N$, which the authors connect to the stringy exclusion principle and to possible modifications of semiclassical Hawking radiation arguments.
The method extends to supersymmetric orbifolds by replacing the identity insertion at each puncture with a charge operator built from bosonized fermions.

Reading between the lines

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

The genus expansion here has a different origin from the $1/N$ genus expansion of Yang–Mills: it comes from the topology of the cover, not from double-line Feynman diagrams. Whether the two expansions are the same expansion seen from two sides is a natural question the paper raises but does not settle.
If the sphere term really depends only on $c$, then a twist three-point function in a symmetric orbifold of $K3$ is determined by the same formula as for a single free boson, up to a power of $c$. That is a sharp, checkable statement: a direct free-field computation at small $N$ should reproduce the same numbers.
The suppression of the coupling at twist orders of order $N$ is stated for the bosonic theory, but the combinatorial factor driving it is group-theoretic and should survive supersymmetry. If so, it is a concrete prediction about the deformation away from the orbifold point, testable against supergravity only once the $R$-charge dependence is included.
The paper leaves the normalization of the operator inserted at infinity handled by a ratio of correlators rather than by an absolute definition. A cleaner treatment of the puncture at infinity might remove the residual dependence on the regularization parameters that the authors check cancels but do not derive from first principles.

Original abstract

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle.

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.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.37 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.40 · compares with prior results 0.30 · 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 develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle.

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 develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold.	contribution 0.98	0.95	0.23	asserted 1.00
s1	The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions.	method 0.98	0.84	0.15	asserted 1.00
s2	Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g.	result 0.74	0.86	0.21	asserted 1.00
s3	For large N, this genus expansion coincides with a 1/N expansion.	result 0.68	0.74	0.10	asserted 1.00
s4	The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT.	result 0.94	0.85	0.11	asserted 1.00
s5	For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions.	contribution 0.52	0.95	0.09	asserted 1.00
s6	The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model.	result 0.83	0.81	0.07	asserted 0.99
s7	We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle.	result 0.55	0.92	0.19	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.91 · evidence from proof or derivation 1.00.

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arXiv listing abstract v3

not examined

full text
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references and citing sentences
relations to other papers

levels run

P abstract

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T body sentences
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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

Figures

**Figure 1.** The factor (8.4) as function of n for N¯ = 1000. If the CFT 3-point function is indeed not renormalized for finite N, then the above result has interesting implications. The coupling between three gravitons would then be a constant for low energies (n << N¯) but would drop rapidly for high energies. Thus the behavior of high frequency modes would not follow a naive ‘equivalence principle’. This issue may be relevant to Hawking’s derivation of black hole radiation, where we need to make a change of coordinates to study the high frequency modes near the horizon. For these modes to…

Figures reproduced from arXiv:hep-th/0006196 by the authors.

References

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Diagrams for Symmetric Product Orbifolds
hep-th 2009-05 accept novelty 7.0 of 10

Correlators of twist fields in symmetric product orbifolds can be written as finite sums of diagrams, one per branched covering, with a computable N-dependence and an explicit Heun-equation algorithm for four-point ge...
Radiation from the non-extremal fuzzball
hep-th 2007-11 conditional novelty 7.0 of 10

The classical ergoregion instability of non-extremal fuzzball geometries equals the Hawking radiation from those microstates, with emission rate Gamma = 2 omega_I.
Dual geometries for a set of 3-charge microstates
hep-th 2004-05 accept novelty 7.0 of 10

Exact extremal D1-D5-P geometries dual to spectral-flowed CFT microstates are smooth, with no horizon and no singularity.
virasoro_blocks: Software for the 2d bootstrap
hep-th 2026-10 conditional novelty 6.0 of 10

Virasoro_blocks makes Virasoro conformal blocks usable in semidefinite-program bootstraps and yields scalar-gap and moment bounds that converge toward, and are saturated by, known 2D CFTs including Liouville theory.
Thermal Giant Graviton Expansion
hep-th 2026-10 accept novelty 6.0 of 10

Exact finite-N and infinite-N expansions of free SYM partition functions are derived from chiral holography, with D-instantons resumming to the Hagedorn temperature.
Neural Spectral Bias and Conformal Correlators II: Modular and Annulus Bootstrap
hep-th 2026-07 conditional novelty 6.0 of 10

Lightweight neural nets with spectral bias reconstruct full 2d CFT torus and annulus partition functions from crossing, a gap, and a single interior anchor to sub-percent accuracy on known theories.
Signatures of Quantum Chaos in the D1D5 System
hep-th 2026-05 unverdicted novelty 6.0 of 10

Finite-N non-planar mixing in the D1D5 CFT produces level repulsion and random-matrix statistics in symmetry-resolved sectors, while the planar large-N limit yields Poisson statistics.
Exploring the twisted sector of $\mathbb{Z}_{L}$ orbifolds: Matching $\alpha'$-corrections to localisation
hep-th 2025-12 unverdicted novelty 6.0 of 10

For generic Z_L orbifolds, naive reduction of the 10d (α')^3 correction fails to match localisation results for twisted half-BPS correlators except at special L values; expanding a twisted Virasoro-Shapiro amplitude r...
The Triplet Perturbation of the Symmetric Orbifold
hep-th 2025-09 conditional novelty 6.0 of 10

The triplet perturbation of the T4 symmetric orbifold is shown to preserve the same integrable structure as the singlet and is identified with the self-dual R-R 2-form modulus in AdS3/CFT2.
On the CFT dual of superstring on AdS$_3$
hep-th 2025-04 conditional novelty 6.0 of 10

This paper verifies, at second order in conformal perturbation theory, that the proposed marginal deformation of a symmetric orbifold CFT reproduces the residues of three-point superstring correlators on AdS3 x S3 x T4.
Symmetric orbifold OPE from string theory
hep-th 2025-04 conditional novelty 6.0 of 10

The worldsheet OPE of delta-function vertex operators in AdS3 string theory captures the longest single-cycle term of the symmetric orbifold OPE, with shorter cycles generated by screening operators.
Holographic covering and the fortuity of black holes
hep-th 2024-02 conditional novelty 6.0 of 10

BPS states in holographic CFTs split into monotone states dual to smooth horizonless geometries and fortuitous states that carry the black hole entropy.
Correlators of the symmetric product orbifold
hep-th 2019-11 accept novelty 6.0 of 10

Null vectors of the fractional Virasoro algebra yield differential equations that fix twist-field correlators in the symmetric product orbifold, reproducing and extending known results from symmetry alone.
Quasinormal modes of supersymmetric microstate geometries from the D1-D5 CFT
hep-th 2019-08 conditional novelty 6.0 of 10

In the near-decoupling limit, the scalar quasinormal mode spectrum of GMS microstate geometries is reproduced exactly by D1-D5 orbifold CFT emission amplitudes, including the slow-decaying ERS modes.
AdS$_3$ Holography at Dimension Two
hep-th 2019-04 accept novelty 6.0 of 10

A complete holographic dictionary for dimension (1,1) chiral primaries in the D1-D5 system is derived, calibrated on known two-charge geometries, and confirmed exactly on independent two-charge states and on several s...
Permutation Orbifolds in the large N Limit
hep-th 2015-09 conditional novelty 6.0 of 10

Permutation orbifolds built from oligomorphic group families have finite large-N spectra, and those acting democratically have correlators that factorize into generalized free fields.
AdS3 Holography for 1/4 and 1/8 BPS geometries
hep-th 2015-07 accept novelty 6.0 of 10

The paper proposes and tests a CFT dictionary for 1/8-BPS superstrata geometries, showing that holographic one-point functions and small-interval entanglement entropy match orbifold-CFT calculations, including a twist...
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.
Mutual information after a local quench in conformal field theory
hep-th 2013-11 conditional novelty 6.0 of 10

After a local quench in a 2d CFT, two-interval mutual information is separation-independent at leading order, while the falling-mass holographic model of the same quench yields mutual information that decays logarithm...
Holographic entanglement beyond classical gravity
hep-th 2013-06 conditional novelty 6.0 of 10

One-loop bulk corrections to holographic entanglement entropy reproduce known universal CFT terms and produce new finite-size and thermal-state effects invisible at leading order.
Entanglement Entropy at Large Central Charge
hep-th 2013-03 conditional novelty 6.0 of 10

At large central charge, the entanglement entropy of N disjoint intervals in a 2d CFT equals a sum of single-interval entropies selected by the dominant OPE channel, reproducing the Ryu-Takayanagi minimal-surface formula.
D1-D5-P microstates at the cap
hep-th 2012-11 conditional novelty 6.0 of 10

Fractional spectral flow states in the D1-D5-P orbifold CFT are identified as the duals of two-center Bena-Warner microstate geometries, with the massless scalar spectra matching exactly.
Kerr/CFT, dipole theories and nonrelativistic CFTs
hep-th 2011-08 conditional novelty 6.0 of 10

A class of warped AdS3 supergravity backgrounds is identified as a deformation of the DLCQ of the D1-D5 CFT by a single (1,2) operator, proposing nonrelativistic CFT duals for Kerr/CFT and dipole backgrounds.
Deforming the D1D5 CFT away from the orbifold point
hep-th 2010-02 conditional novelty 6.0 of 10

Acting with the twist deformation operator on two Ramond-ground-state copies of the c=6 CFT produces a squeezed state whose bosonic and fermionic pair coefficients are computed in closed form.
Metric of the multiply wound rotating string
hep-th 2001-05 accept novelty 6.0 of 10

The supergravity solution for a multiwound string with maximal angular momentum spreads the string strands over a torus, and dualities map it to the D1-D5 black hole system.
Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry
hep-th 2001-03 conditional novelty 6.0 of 10

The authors derive three-point functions of twist-field chiral operators in N=4 supersymmetric M^N/S^N orbifolds at large N, finding a universal expression independent of the internal manifold M.
CFT Correlators from (0,2) Heterotic String
hep-th 2024-12 conditional novelty 5.0 of 10

The (0,2) heterotic string amplitudes with positive winding are shown to match correlation functions of the symmetric product CFT (ML)^N/S_N, confirming a prior proposal.
Higher-point conformal blocks and entanglement entropy in heavy states
hep-th 2016-01 conditional novelty 5.0 of 10

Higher-point conformal blocks with two heavy operators factorize into products of four-point blocks in the heavy-light limit, and the same factorization reproduces holographic entanglement entropy for many disjoint in...
Holographic description of non-supersymmetric orbifolded D1-D5-P solutions
hep-th 2015-08 accept novelty 5.0 of 10

The orbifolded JMaRT supergravity solutions are identified with fractional-spectral-flow states of the D1-D5 orbifold CFT, with massless scalar emission spectra and rates matching exactly between gravity and CFT in th...
Nuts and Bolts for Creating Space
hep-th 2014-09 conditional novelty 5.0 of 10

Bulk points and distances in AdS3 can be defined purely from boundary entanglement entropies via a variational principle, with the triangle inequality following from strong subadditivity.
Operator mixing for string states in the D1-D5 CFT near the orbifold point
hep-th 2012-11 conditional novelty 5.0 of 10

The string state ∂X∂X ∂̄X∂̄X in the D1-D5 CFT mixes with a (2,2) quasi-primary at first order in the deformation parameter, providing evidence that it acquires an anomalous dimension.
3-charge geometries and their CFT duals
hep-th 2004-06 conditional novelty 5.0 of 10

Two families of D1-D5-P microstate geometries are constructed and shown to cap off smoothly, with their CFT duals identified via travel-time and absorption-threshold matching.
Emergent Spacetime and Holographic CFTs
hep-th 2011-01 conditional novelty 4.0 of 10

Factorization of light-operator correlators requires infinite central charge, and the factorized sector is naturally reorganized as free fields and Witten diagrams in an emergent anti-de Sitter space.
Microscopic Formulation of Black Holes in String Theory
hep-th 2002-03 accept novelty 4.0 of 10

The low-energy conformal field theory of the D1-D5 brane system, with central charge 6Q1Q5, reproduces the five-dimensional black hole's Bekenstein-Hawking entropy and its Hawking rate, including four scalar modes tha...
Using the D1D5 CFT to Understand Black Holes
hep-th 2010-12 conditional novelty 3.0 of 10

The D1D5 orbifold CFT reproduces, mode by mode, the emission spectrum of the JMaRT horizonless geometries, supporting the reading of their ergoregion instability as Hawking radiation from black hole microstates.

See all 64 Pith citations

How later papers used it

178 later papers cite it

Evidence: substantial. 161 of the citing papers share no author with it, and 70 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 497 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 method or tool and 1 used its data or values. 1 of them appears under more than one label.

Uses its method or tool 3 of 65 papers with this label

Computed the correlator of local twist operators using techniques from this paper.

Evolution of entanglement entropy in the D1-D5 brane system (2011) · 1.00 · paraphrased: the licence does not allow quoting
Applied this paper's procedure to determine the correlation function as a function of y_ℓ, z_ν and w_ν.

Correlation functions of symmetric orbifold from AdS$_3$ string theory (2020) · 0.99 · paraphrased: the licence does not allow quoting
Constructed the map from the base space to the covering space such that there are distinguished points in the covering space, following this paper.

Twist-nontwist correlators in M^N/S_N orbifold CFTs (2012) · 0.84 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 7 papers with this label

Read this from equation (3.18) of this paper, recalling that the bare twists have weight h=(c/24)(n-1/n)=3/8 for c=6, n=2.

Twist-nontwist correlators in M^N/S_N orbifold CFTs (2012) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

167 arXiv papers cite this in 484 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 · 268 sentences without a confident label

Builds on it 5 papers

The result of the procedure is [equation] which is a generalization of the result in equation (7.23) of [ref] .

The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$ · Four point function from Lunin-Mathur · 0.82
This generalizes the expressions derived in [ref] to non-holomorphic fields.

Conformal Perturbation Theory for Twisted Fields · Twisted fields and the cover map · 1.00
The partition function then becomes a sum over $G$ partition functions on branched covers of $M$ over $L$, i.e. [equation] Note that this is essentially the three-dimensional generalization of the covering space construction for calculating correlation functions of twist fields in two-dimensional CFTs [ref] .

The Lion, the Witch, and the Wormhole: Ensemble averaging the symmetric product orbifold · Vortices · 0.81

Uses its method or tool 63 papers

This is what we compute in the present paper, using the `covering surface technique' [ref] together with the `stress-tensor method' [ref] .

Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$ · Introduction · 1.00
To compute the four-point function we need to find a map to the covering space, and then compute the Liouville action associated with the map [ref] .

Evolution of entanglement entropy in the D1-D5 brane system · The twist correlator · 0.99
In what follows here, we will use heavily the pioneering work of Lunin and Mathur on computing three point functions in (super)conformal orbifold theories [ref] .

Correlation functions in the D1-D5 orbifold CFT · Introduction · 0.94

Uses its data or values 7 papers

We read this from equation (3.18) of [ref] , recalling that the bare twists have weight $h=(c/24)(n-1/n)=3/8$ for $c=6,n=2$.

Twist-nontwist correlators in M^N/S_N orbifold CFTs · Non-twist operator insertions · 0.97
The two point functions of regularised twist operators at finite separation are given by [ref] ⟨σ^ϵ_m (0) σ^ϵ_m (y) ⟩= y^- (m - 1/m) ( m^2 e^- (m-1)^2/m) Q^1-m where $Q$ depends on the regularization.

Correlation functions in the D1-D5 orbifold CFT · Twist operator correlator · 0.91
so we obtain [equation] Before computing the spin correlator in Eq. [ref], we recall the value of the twist fusion coefficient we require [ref] , [equation] The map from the $z$-plane to the covering space used to compute this is given in [ref] .

AdS$_3$ Holography at Dimension Two · Expectation value of $Σ_3^00$ on a 3-charge state · 0.92

Compares with it 11 papers

They precisely agree with the predictions from the holographic CFT at the symmetric orbifold point [ref] , and complete the exact (large $N$) holographic matching of the full AdS$_3$/CFT$_2$ chiral ring.

Spectral flow and the exact AdS$_3/$CFT$_2$ chiral ring · Discussion · 0.96
(5.30) in [ref] , we have included an additional factor $w_3^-w_3-1$ in the following equation.

Correlators of long strings on AdS$_3\times$S$^3\times$T$^4$ · Matching the correlators at the leading order · 0.84
Here we evaluate spectral flow conserving three-point functions on the sphere involving spectral flow images of chiral primary string states in the Neveu-Schwarz (NS) and Ramond (R) sectors of the SL(2, $ℝ)$ WZNW model in order to complete the construction of these amplitudes in the full string theory and compare them with the conjectured dual correlators in the symmetric orbifold of T$^4$ obtained in [ref] .

Three-point functions in superstring theory on AdS3xS3xT4 · Introduction · 0.96

Cites it as support 3 papers

This cements the identification of the covering space with the worldsheet as conjectured already in [ref] .

Twistor Coverings and Feynman Diagrams · Symmetric orbifold CFT correlators and branched coverings · 0.99
We argued this on the basis of the universality of the four-point function of bare twists (and therefore their fractional excitations) at large $N$ [ref] , along with our calculations which were performed to several non-trivial orders.

The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry · Fractional spectral flow · 0.98
Building the $S_N$ invariant objects introduces certain combinatoric factors, and these factors are exactly what lead to a suppression of factors of $1/N$ allowing one to concentrate on the case of a spherical cover [ref] .

Bosonization, cocycles, and the D1-D5 CFT on the covering surface · Introduction · 0.96

Cites it as background 56 papers

Recall from [ref] that different families of exchange channels result from different limits of the same four point function.

The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry · Three-point and four-point function generalities · 0.94
We will first review the general construction in the case of symmetric product orbifolds (see, e.g. [ref] ) before discussing some specific aspects that concern the specific correlations functions [ref] that arise in the context of our perturbative deformation.

Engineering Perturbative String Duals for Symmetric Product Orbifold CFTs · Correlations functions and covering maps · 0.86
A very special case is that of $k=1$; in that case, the string model is dual [ref] to a particularly simple (and well-studied, see e.g. [ref] ) CFT, the symmetric product orbifold CFT of $T^4$.

Comments on Integrability in the Symmetric Orbifold · Introduction and summary · 0.88

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.

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