Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

On the CFT dual of superstring on AdS$_3$

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that the proposed exactly marginal operator deforming the symmetric orbifold CFT dual to superstring on AdS$_3\times S^3\times T^4$ is verified by a term-by-term match of next-to-leading residues of three-point…

desk verdict A technically impressive second-order matching that likely verifies the proposed SUSY marginal operator, but the decisive covering-map identities are only numerically checked and the integration-by-parts step is asserted, so the case is solid but conditional. read the letter →

arxiv 2504.20227 v3 pith:PP2AJFZT submitted 2025-04-28 hep-th math-phmath.MP

Zhe-fei Yu This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords AdS3/CFT2symmetricorbifoldcoveringmapsexactlymarginaldeformationsuperstringcorrelatorsconformalperturbationtheoryspectralflowpicturechanging
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims to verify the proposed exactly marginal deformation of the symmetric-orbifold CFT that is dual to superstring theory on AdS$_3\times S^3\times T^4$ with pure NS-NS flux. It compares residues of three-point correlators at their next-to-leading pole: on the string side these are extracted from known spectrally flowed correlators and written as integrals, and on the CFT side they are produced by a second-order conformal perturbation computation. After a change of variables the two integrands are shown to agree term by term, which fixes the picture-changing ambiguity on the string side and the normalization of the deformation parameter. The decisive new ingredient is a set of covering-map identities involving the second Taylor coefficients at the ramified points, so the check goes one order beyond the bosonic duality and beyond earlier leading-order supersymmetric matching.

What carries the argument

The load-bearing objects are the functions $X_i(y_1,y_2,y_3)$ built from the $P_{w_1,w_2,w_3}$ coefficients that appear in the exact three-point functions of spectrally flowed operators in the $SL(2,\mathbb{R})$ WZW model, together with their sign-flipped 'conjugates' $\tilde X_i$ introduced in the paper. On the CFT side the same matching data come from covering maps with ramification indices $w_i$ at three twist insertions and two insertions of the marginal operator; near the latter points the map expands as $\Gamma(z)=\xi_i + A_i(z-\eta_i)^2 + B_i(z-\eta_i)^3+\cdots$, and $C_i\equiv -3B_i/(4A_i)$ measures the failure of the lifted marginal operator to be a Virasoro primary. The identities (4.23) and (4.38) tie these second-order Taylor data to $X_i$ and $\tilde X_i$, converting an intractable five-ramified-point problem into algebra. The regular/irregular split of the ten coefficient functions is organized precisely around whether $C_1,C_2$ appear.

What would settle it

Take a generic odd triple, for instance $(w_1,w_2,w_3)=(3,3,5)$, construct the unique covering map by the residue method of the paper's appendix, expand it to third order at the two marginal insertions, and numerically test identities (4.23) and (4.38) and the derived coefficient equalities (4.36) and (4.40) to high precision with the condition $X_{123}=0$ imposed. A single generic triple where these identities fail settles the claim negatively; conversely, an analytic proof for all odd triples would close the gap the paper leaves open.

Watch

Extended reading notes

Core claim

The central claim is that the operator $\Phi$ defined in (3.25) — a linear combination of super-descendants of BPS twist-2 operators, obtained by acting on $\Psi_{\alpha A}$ with holomorphic and anti-holomorphic $N=4$ supercurrents — is the correct exactly marginal operator deforming the symmetric orbifold. The evidence is a quantitative match of residues. The string-side residue is written as an integral whose integrand is not picture-choice invariant; the paper argues the correct integrand is a linear combination $\alpha\hat F^{(1)}+\beta\hat F^{(2)}+\gamma\hat F^{(3)}$ with $\alpha+\beta+\gamma=1$, extended by integration by parts so $\alpha,\beta,\gamma$ may be functions, and with the mass-shell condition used to eliminate $h_i$ dependence. The CFT-side residue is a second-order conformal perturbation integral of a five-point function in the symmetric orbifold, evaluated by lifting to a covering surface. The paper shows that after identifying the integration variables $(a_1,a_2)$ with $(y_1,y_2)$, the ten coefficient functions of $\frac{j_1 j_2}{k}$, $\frac{j_1^2}{k}$, $\frac{j_2^2}{k}$, $\frac{j_1}{k}$, $\frac{j_2}{k}$, $\frac{1}{k}$, $1$, $k$, $j_1$, $j_2$ match individually; the matching of the four irregular terms uses new identities, (4.23) and (4.38), expressing $C_i=-3B_i/(4A_i)$ and the derivatives $\partial_{a_1}\alpha$, $\partial_{a_2}\beta$ in terms of $X_i$ and their conjugates $\tilde X_i$.

Load-bearing premise

The load-bearing premise is that the new covering-map identities (4.23) and (4.38) hold for all odd winding numbers $w_i$ with $w_1+w_2+w_3$ odd; they are checked numerically in the ancillary notebook, with analytic proofs only for the edge cases $w_1+w_2+1=w_3$ and $w_1=w_2=w_3=1$, and if they fail for a generic triple the irregular residues would not match and the verification would collapse.

Editorial extensions

If this is right

  • If the matching is correct, the operator (3.25) is confirmed as the exactly marginal deformation of the symmetric orbifold dual, at least to second order for correlators with odd $w_i$ and odd $w_1+w_2+w_3$.
  • The correct string-side residue integrand is a nontrivial linear combination of picture choices, not any single picture, so future string-side computations must confront picture-changing ambiguity in the integral form.
  • The mass-shell condition is essential in the supersymmetric matching, unlike in the bosonic case, so the deformed CFT check probes the internal $S^3\times T^4$ data, not just the AdS$_3$ sector.
  • The same method should transfer to superstrings on AdS$_3\times X$: the string-side residue is universal, and the matching fixes the structure of the deforming operator as a linear combination of super-descendants in the twist-2 sector.
  • The identities (4.23) and (4.38) give a concrete mathematical prediction about any covering map with five ramified points: its second Taylor coefficients are expressible through the $X_i$ and $\tilde X_i$ building blocks.

Reading between the lines

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

  • A testable extension is to prove (4.23) and (4.38) analytically for all odd triples using the residue construction of the appendix; the edge-case checks suggest such a proof would amount to a purely algebraic identity among $X_i$, $\tilde X_i$, and the condition $X_{123}=0$.
  • Because the identities (4.38) hold only for odd $w_i$, the parity of winding numbers is entangled with the mathematics; this suggests the even-$w$ case needs a genuinely different integrand and may single out the correct deformation operator more sharply than the odd case does.
  • The paper leaves open the sign of the deformation parameter $\mu$; a first-order computation for correlators with even $w_1+w_2+w_3$ would fix the sign and at the same time discriminate the full four-term operator (3.25) from two-term non-singlet candidates.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper extends the perturbative AdS3/CFT2 matching of [6,50] from leading order to second order in the conformal perturbation expansion, with the stated goal of verifying the marginal operator Φ that deforms the symmetric orbifold CFT dual to superstring theory on AdS3×S3×T4 with pure NS-NS flux. On the string side, the author extracts the residue of the three-point correlator of spectrally flowed operators O^w_{j,h} at the next-to-leading pole (m=2) and expresses it as an integral. Since picture changing makes the integrand non-unique, an ansatz is made that linearly combines three picture choices with coefficients α, β, γ (initially constants, later promoted to functions of the integration variables). On the CFT side, the corresponding residue is computed by a second-order conformal perturbation computation, i.e., a five-point function in the undeformed symmetric orbifold containing two insertions of Φ, evaluated with covering maps. A key feature is that the lifted marginal operator is not a Virasoro primary on the covering surface, so the result depends on the second Taylor coefficients C1, C2 of the covering maps at the ramified points.

Significance. If the identities (4.23) and (4.38) hold for generic odd windings, this is a significant step for the AdS3/CFT2 program: it is the first quantitative check that directly involves the marginal operator defining the deformation, since the 0th-order matching of [50] inserts no such operator. The paper identifies structures that will matter at higher orders and in other backgrounds: the non-uniqueness of the string-side integrand under picture changing; the necessary use of the mass-shell condition (absent in the bosonic case); and the non-primary nature of the lifted marginal operator, which couples the CFT computation to second-order data of the covering maps. The matching is performed at the level of integrands rather than integrals, which is considerably stronger than matching integrated residues, and the ancillary Mathematica notebook documents the numerical verification of the key identities. The author also explicitly acknowledges the scope and limitations of the computation (Section 5.1).

major comments (3)
  1. [§4.3, Eqs. (4.23) and (4.38)] The matching of the four irregular coefficients—the part of the verification that carries the distinctive supersymmetric physics—rests entirely on the identities (4.23) and (4.38), together with the linear relation (4.25). The manuscript states that (4.23) is checked numerically in the ancillary Mathematica notebook, with analytic proofs only for the edge case w3 = w1+w2+1 (where the relevant P functions vanish and X_i reduce to constants) and for w1 = w2 = w3 = 1; the windings covered by the numerical check are not specified. For (4.38), no analytic verification is presented, and the manuscript notes that (4.38) holds only when all w_i are odd, underscoring its delicacy. Since the irregular terms are precisely those containing the second Taylor coefficients C1, C2 of the covering maps—the terms that distinguish the supersymmetric case from the bosonic one—a failure of (4.23) or (4.38) for some generic odd configuration (e.g., (3,5,7)) would invalidate the verification of Φ. I request an analytic derivation of (4.23) and (4.38), perhaps from the covering-map differential equation (C.4)–(C.8) combined with (4.25); at minimum, the numerical verification should be made systematic over a range of winding triples and the validity conditions of the identities stated precisely.
  2. [§2.3, Eqs. (2.42)–(2.45)] The integration-by-parts step that justifies replacing F^(3) by the general ansatz F, and thereby legitimizes the α, β, γ-dependent form of the string-side integrand, requires the boundary terms in (2.42) to vanish. The manuscript asserts that F should be 'an arbitrary function that makes the possible boundary terms in (2.42) vanish,' but the functions α, β, γ that actually produce the matching are non-trivial functions of the integration variables, fixed only later in (4.16) in terms of η1, η2. The vanishing of the boundary terms for these specific functions is never demonstrated. If the boundary terms do not vanish for the α, β, γ of (4.16), the equivalence leading to (2.46) does not hold and the string-side integrand used in the matching would not represent the physical residue. The author should show explicitly that the boundary terms vanish for the fixed α, β, γ (or state the boundary conditions on y1, y2 under which they do).
  3. [Abstract and §5.1] The abstract states that the calculation 'verifies the proposed marginal operator in the dual CFT,' but Section 5.1 concedes that the four terms in (3.26) give identical contributions to the computed correlators, so the second-order matching cannot distinguish the singlet combination (3.25) from, e.g., the two-term operator (5.1). The rejection of (5.1) rests on an appeal to global symmetries ('intuitively it should not be the correct marginal operator'), not on the computed correlators. The headline claim should therefore be qualified: the computation verifies the structural form of the deformation (a superdescendant of the twist-2 BPS operator with the correct lifting behavior) and is consistent with the proposed singlet operator Φ, but it does not by itself single out (3.25) among the admissible combinations. This qualification should appear in the abstract and conclusion as well as in Section 5.1.
minor comments (6)
  1. [§3.3.2, Eq. (3.81)] In the first bracket of C^CFT_Γ[1], the term '-1/(η1(η2-1))' appears twice with identical form; given the pattern of the C1- and C2-terms in the same equation and the simplified form (4.37), one of the two repetitions is likely a typo (possibly '-1/(η2(η1-1))'). Please check this expression.
  2. [§2.2, Eqs. (2.25)–(2.26)] The text below (2.25) refers to 'F_y(y1,y2,y3) ... the correlator in the y-basis' without defining F_y; since F is defined in (2.26) and B in (2.22), the notation should be clarified to avoid ambiguity about which function has no h_i dependence.
  3. [§3.3.1] The normalization bookkeeping in the lifting of the marginal operator—the prefactor 2^{-1/2} in (3.43), the rescaling 'Φ → 2^{1/2} Φ', and the prefactors 2^{h1+h2/2-1} and w^{hα/w-1} in footnotes 13 and 14—is hard to follow. A short summary of the fractional-mode conventions used to define ΨαA and V^{(w)}_α, including the role of the w^{1-h} factor in (3.16), would make the computation checkable by the reader.
  4. [§4.2, below Eq. (4.18)] The sentence 'We expect the one with minus sign should be the correct one' leaves the sign of µ undetermined by the m=2 computation; since a wrong sign of µ would propagate to all higher-order checks, the ambiguity should be flagged as a limitation in the main text rather than left as an expectation.
  5. [Abstract and title] There is an errant space before the subscript in 'AdS 3×S3×T4' in the abstract and at several points in the main text (e.g., page 2, Section 2.1); this formatting artifact should be fixed in the final version.
  6. [§4.1, Eq. (4.8)] The chain of equalities expressing 1/R in three ways relies on the identities (4.3), (4.4), and on the subsequent equations (4.9); a brief indication of which identity is used at each equality would help the reader follow Section 4.1, which is otherwise quite dense.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the CFT side is computed independently from the proposed marginal operator, and the string-side integrand parameters are fitted before the remaining coefficients are checked. The main caveats are numerical verification of the new covering-map identities, not circularity.

full rationale

The derivation is not circular. The CFT residue is obtained by a second-order conformal perturbation computation (Section 3.3) using the proposed operator Phi in (3.25); no string-side data enter this calculation. The string residue (2.57) starts from the correlator computed in [50] and then chooses a non-unique integrand representative with parameters alpha, beta, gamma (Section 2.3). These parameters are not hidden predictions: they are fixed in (4.14)-(4.17) by matching the three regular coefficients (j1 j2/k, j1^2/k, j2^2/k), together with alpha+beta+gamma=1 and the normalization condition; the deformation parameter mu is determined at the same point. The three remaining regular coefficients then follow from the same algebraic relations (4.20)-(4.21) on both sides, and the four irregular coefficients are checked using the independent covering-map identities (4.23), (4.36) and (4.38). None of these identities is equivalent to the physical matching claim by construction; they are mathematical statements about Taylor coefficients of covering maps, verified numerically in the ancillary notebook. The chief weakness is that (4.23) and (4.38) lack analytic proofs for generic odd w_i, and (4.38) is asserted to hold only for all-odd w_i; this is a correctness and rigor gap, not a circularity. Self-citations to [50] supply the starting string correlator and the leading-order matching but do not assume the next-to-leading verification of the marginal operator.

Assumptions & free parameters 1 free parameters · 6 assumptions · 1 invented entities

The central claim depends on standard background results (spectral flow correlators, covering map method, duality dictionary) and on the proposed exactly marginal operator. The only parameters fitted to the comparison are the ansatz coefficients alpha, beta, gamma; mu is an output. The new mathematical identities are ad hoc to this paper and only numerically verified.

free parameters (1)
  • alpha, beta, gamma (ansatz coefficients) = Functions of (eta1, eta2) given in (4.16); alpha+beta+gamma=1
    Introduced in (2.39) as a linear combination of three picture choices for the string-side integrand. The paper states they "can only be fixed when compared with the CFT side" and fixes them by requiring the coefficients of j1j2/k, j1^2/k, j2^2/k to match (4.14)-(4.16).
assumptions (6)
  • standard math Closed formula for 3-point functions of spectrally flowed operators in SL(2,R) WZW (from [37], proved in [38])
    Used in eq (2.19) for the string-side correlator; external theorem not reproven here.
  • domain assumption Lunin-Mathur covering map formula for symmetric orbifold correlators (eq 3.9)
    Standard method for computing large-N symmetric orbifold correlators; used for the five-point function.
  • domain assumption Identification of long-string vertex operators with V_alpha^(w) in the twist-w sector (from [50,61])
    Part of the duality dictionary; maps string states to CFT operators.
  • domain assumption The deforming operator Phi in (3.25) is exactly marginal
    Proposed in [6]; assumed to define the deformed theory. The paper verifies it but does not independently prove exact marginality.
  • domain assumption Large N limit: genus-zero covering surfaces dominate
    Standard large-N expansion in symmetric orbifolds; the paper restricts to this limit.
  • ad hoc to paper Identities (4.23), (4.38), and (4.25) relating covering map data and X_i, \tilde X_i
    New identities introduced here; only numerically verified, with analytic proof in special cases; needed for the irregular-term matching.
invented entities (1)
  • Conjugate functions \tilde X_i
    purpose: Compact expression of string-side irregular coefficients and statement of the novel covering-map identities (4.23)
    Defined in (2.55) by flipping a sign in X_i; no independent falsifiable handle outside this paper; their validity is checked numerically in the attached Mathematica notebook.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the CFT dual of superstring on AdS$_3$." pith.science (2026). https://pith.science/paper/PP2AJFZT

@misc{pith2026250420227,
  author       = {Pith},
  title        = {Pith review of: On the CFT dual of superstring on AdS$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PP2AJFZT}},
  note         = {Machine review of arXiv:2504.20227}
}
abstract

In this work, we study the proposed duality between superstring on AdS$_3\times$S$^3\times\mathbb{T}^4$ with pure NS-NS flux and a deformed symmetric orbifold CFT. We extract the residues of 3-point string correlators at their next-to-leading poles, which can be expressed as integrals. Because of picture changing, the integrand is not unique. We make an ansatz for its proper form which linearly combines three different picture choices. On the CFT side, we obtain the corresponding residues by doing a conformal perturbation computation at the second order. The result can also be expressed as integrals, with the integrand being a five point function in the symmetric orbifold theory, which is calculated using covering maps. After unifying the integration variables of the two sides, we find that the two integrands match precisely, due to some novel mathematical identities of covering maps. Our calculation verifies the proposed marginal operator in the dual CFT of superstring on AdS$_3\times$S$^3\times\mathbb{T}^4$ and could be generalized to the CFT duals of superstrings on general backgrounds AdS$_3\times X$ with few modifications.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Covering space maps for $n$-point functions with three long twists

    hep-th 2025-07 conditional novelty 7.0 of 10

    Explicit covering-space maps for three long twists plus any number of twist-2 operators are constructed, yielding closed-form four- and five-point bare twist correlators in the ΔN=1,2 cases.

Reference graph

Works this paper leans on

74 extracted references · 11 canonical work pages · cited by 1 Pith paper

  1. [50]

    Yu and C

    Z.-f. Yu and C. Peng,Correlators of long strings on AdS 3×S3×T4,JHEP01(2025) 017, [arXiv:2408.16712]

    arXiv 2025

  2. [1]

    J. M. Maldacena,The Large N limit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231–252, [hep-th/9711200]

    arXiv 1998

  3. [2]

    Seiberg and E

    N. Seiberg and E. Witten,The D1 / D5 system and singular CFT,JHEP04(1999) 017, [hep-th/9903224]

    arXiv 1999

  4. [3]

    M. R. Gaberdiel and R. Gopakumar,Tensionless string spectra on AdS 3,JHEP05(2018) 085, [arXiv:1803.04423]

    arXiv 2018

  5. [4]

    Eberhardt, M

    L. Eberhardt, M. R. Gaberdiel, and R. Gopakumar,The Worldsheet Dual of the Symmetric Product CFT,JHEP04(2019) 103, [arXiv:1812.01007]

    arXiv 2019

  6. [5]

    Eberhardt, M

    L. Eberhardt, M. R. Gaberdiel, and R. Gopakumar,Deriving the AdS 3/CFT2 correspondence,JHEP02(2020) 136, [arXiv:1911.00378]

    arXiv 2020

  7. [6]

    Eberhardt,A perturbative CFT dual for pure NS–NS AdS 3 strings,J

    L. Eberhardt,A perturbative CFT dual for pure NS–NS AdS 3 strings,J. Phys. A55(2022), no. 6 064001, [arXiv:2110.07535]

    arXiv 2022

  8. [7]

    Balthazar, A

    B. Balthazar, A. Giveon, D. Kutasov, and E. J. Martinec,Asymptotically free AdS 3/CFT2, JHEP01(2022) 008, [arXiv:2109.00065]

    arXiv 2022

Show all 74 references
  1. [8]

    E. J. Martinec,A defect in AdS 3/CFT2 duality,JHEP06(2022) 024, [arXiv:2201.04218]

    2022 arXiv

  2. [9]

    Chakraborty, A

    S. Chakraborty, A. Giveon, and D. Kutasov,Effective AdS 3/CFT2,JHEP03(2025) 030, [arXiv:2501.09119]

    2025 arXiv

  3. [10]

    Giveon, D

    A. Giveon, D. Kutasov, E. Rabinovici, and A. Sever,Phases of quantum gravity in AdS(3) and linear dilaton backgrounds,Nucl. Phys. B719(2005) 3–34, [hep-th/0503121]

    2005 arXiv

  4. [11]

    Aharony and E

    O. Aharony and E. Y. Urbach,Type II string theory on AdS3×S3×T4 and symmetric orbifolds,Phys. Rev. D110(2024), no. 4 046028, [arXiv:2406.14605]

    2024 arXiv

  5. [12]

    Knighton,Deriving the long-string CFT in AdS 3,arXiv:2410.16904

    B. Knighton,Deriving the long-string CFT in AdS 3,arXiv:2410.16904

    arXiv

  6. [13]

    Kutasov and N

    D. Kutasov and N. Seiberg,More comments on string theory on AdS(3),JHEP04(1999) 008, [hep-th/9903219]

    1999 arXiv

  7. [14]

    Giveon and D

    A. Giveon and D. Kutasov,Notes on AdS(3),Nucl. Phys. B621(2002) 303–336, [hep-th/0106004]

    2002 arXiv

  8. [15]

    Kim and M

    J. Kim and M. Porrati,On the central charge of spacetime current algebras and correlators in string theory on AdS 3,JHEP05(2015) 076, [arXiv:1503.07186]

    2015 arXiv

  9. [16]

    Eberhardt,Summing over Geometries in String Theory,JHEP05(2021) 233, [arXiv:2102.12355]

    L. Eberhardt,Summing over Geometries in String Theory,JHEP05(2021) 233, [arXiv:2102.12355]

    2021 arXiv

  10. [17]

    Eberhardt,Partition functions of the tensionless string,JHEP03(2021) 176, [arXiv:2008.07533]

    L. Eberhardt,Partition functions of the tensionless string,JHEP03(2021) 176, [arXiv:2008.07533]

    2021 arXiv

  11. [18]

    Giveon, D

    A. Giveon, D. Kutasov, and N. Seiberg,Comments on string theory on AdS(3),Adv. Theor. Math. Phys.2(1998) 733–782, [hep-th/9806194]

    1998 arXiv

  12. [19]

    de Boer, H

    J. de Boer, H. Ooguri, H. Robins, and J. Tannenhauser,String theory on AdS(3),JHEP12 (1998) 026, [hep-th/9812046]

    1998 arXiv

  13. [20]

    J. M. Maldacena and H. Ooguri,Strings in AdS(3) and SL(2,R) WZW model 1.: The Spectrum,J. Math. Phys.42(2001) 2929–2960, [hep-th/0001053]. – 52 –

    2001 arXiv

  14. [21]

    J. M. Maldacena, H. Ooguri, and J. Son,Strings in AdS(3) and the SL(2,R) WZW model. Part 2. Euclidean black hole,J. Math. Phys.42(2001) 2961–2977, [hep-th/0005183]

    2001 arXiv

  15. [22]

    J. M. Maldacena and H. Ooguri,Strings in AdS(3) and the SL(2,R) WZW model. Part 3. Correlation functions,Phys. Rev. D65(2002) 106006, [hep-th/0111180]

    2002 arXiv

  16. [23]

    Giribet and C

    G. Giribet and C. A. Nunez,Aspects of the free field description of string theory on AdS(3), JHEP06(2000) 033, [hep-th/0006070]

    2000 arXiv

  17. [24]

    Giribet and C

    G. Giribet and C. A. Nunez,Correlators in AdS(3) string theory,JHEP06(2001) 010, [hep-th/0105200]

    2001 arXiv

  18. [25]

    Giribet and Y

    G. Giribet and Y. Nakayama,The Stoyanovsky-Ribault-Teschner map and string scattering amplitudes,Int. J. Mod. Phys. A21(2006) 4003–4034, [hep-th/0505203]

    2006 arXiv

  19. [26]

    Ribault,Knizhnik-Zamolodchikov equations and spectral flow in AdS(3) string theory, JHEP09(2005) 045, [hep-th/0507114]

    S. Ribault,Knizhnik-Zamolodchikov equations and spectral flow in AdS(3) string theory, JHEP09(2005) 045, [hep-th/0507114]

    2005 arXiv

  20. [27]

    Giribet,On spectral flow symmetry and Knizhnik-Zamolodchikov equation,Phys

    G. Giribet,On spectral flow symmetry and Knizhnik-Zamolodchikov equation,Phys. Lett. B 628(2005) 148–156, [hep-th/0508019]

    2005 arXiv

  21. [28]

    Minces, C

    P. Minces, C. A. Nunez, and E. Herscovich,Winding strings in AdS(3),JHEP06(2006) 047, [hep-th/0512196]

    2006 arXiv

  22. [29]

    Iguri and C

    S. Iguri and C. A. Nunez,Coulomb integrals for the SL(2,R) WZW model,Phys. Rev. D77 (2008) 066015, [arXiv:0705.4461]

    2008 arXiv

  23. [30]

    W. H. Baron and C. A. Nunez,Fusion rules and four-point functions in the SL(2,R) WZNW model,Phys. Rev. D79(2009) 086004, [arXiv:0810.2768]

    2009 arXiv

  24. [31]

    S. M. Iguri and C. A. Nunez,Coulomb integrals and conformal blocks in the AdS(3) - WZNW model,JHEP11(2009) 090, [arXiv:0908.3460]

    2009 arXiv

  25. [32]

    Giribet,Violating the string winding number maximally in Anti-de Sitter space,Phys

    G. Giribet,Violating the string winding number maximally in Anti-de Sitter space,Phys. Rev. D84(2011) 024045, [arXiv:1106.4191]. [Addendum: Phys.Rev.D 96, 024024 (2017)]

    2011 arXiv

  26. [33]

    Cagnacci and S

    Y. Cagnacci and S. M. Iguri,MoreAdS 3 correlators,Phys. Rev. D89(2014), no. 6 066006, [arXiv:1312.3353]

    2014 arXiv

  27. [34]

    Giribet,One-loop amplitudes of winding strings in AdS 3 and the Coulomb gas approach, Phys

    G. Giribet,One-loop amplitudes of winding strings in AdS 3 and the Coulomb gas approach, Phys. Rev. D93(2016), no. 6 064037, [arXiv:1511.04017]

    2016 arXiv

  28. [35]

    Giribet,Note on the spectral flow operator,Phys

    G. Giribet,Note on the spectral flow operator,Phys. Rev. D100(2019), no. 12 126007, [arXiv:1907.04439]

    2019 arXiv

  29. [36]

    Hikida and T

    Y. Hikida and T. Liu,Correlation functions of symmetric orbifold from AdS 3 string theory, JHEP09(2020) 157, [arXiv:2005.12511]

    2020 arXiv

  30. [37]

    Dei and L

    A. Dei and L. Eberhardt,String correlators on AdS 3: three-point functions,JHEP08(2021) 025, [arXiv:2105.12130]

    2021 arXiv

  31. [38]

    Bufalini, S

    D. Bufalini, S. Iguri, and N. Kovensky,A proof for string three-point functions in AdS 3, JHEP02(2023) 246, [arXiv:2212.05877]

    2023 arXiv

  32. [39]

    V. S. Dotsenko and V. A. Fateev,Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models,Nucl. Phys. B240(1984) 312

    1984

  33. [40]

    V. S. Dotsenko and V. A. Fateev,Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c< 1,Nucl. Phys. B251(1985) 691–734. – 53 –

    1985

  34. [41]

    Dorn and H

    H. Dorn and H. J. Otto,Two and three point functions in Liouville theory,Nucl. Phys. B 429(1994) 375–388, [hep-th/9403141]

    1994 arXiv

  35. [42]

    A. B. Zamolodchikov and A. B. Zamolodchikov,Structure constants and conformal bootstrap in Liouville field theory,Nucl. Phys. B477(1996) 577–605, [hep-th/9506136]

    1996 arXiv

  36. [43]

    Dei and L

    A. Dei and L. Eberhardt,String correlators on AdS 3: Analytic structure and dual CFT, SciPost Phys.13(2022), no. 3 053, [arXiv:2203.13264]

    2022 arXiv

  37. [44]

    Dei and L

    A. Dei and L. Eberhardt,String correlators on AdS 3: four-point functions,JHEP09(2021) 209, [arXiv:2107.01481]

    2021 arXiv

  38. [45]

    Iguri, N

    S. Iguri, N. Kovensky, and J. H. Toro,Spectral flow and the conformal block expansion for strings in AdS 3,arXiv:2406.04247

    arXiv

  39. [46]

    Knighton, S

    B. Knighton, S. Seet, and V. Sriprachyakul,Spectral flow and localisation in AdS 3 string theory,JHEP05(2024) 113, [arXiv:2312.08429]

    2024 arXiv

  40. [47]

    Knighton and V

    B. Knighton and V. Sriprachyakul,Unravelling AdS 3/CFT2 near the boundary,JHEP01 (2025) 042, [arXiv:2404.07296]

    2025 arXiv

  41. [48]

    Hikida and V

    Y. Hikida and V. Schomerus,Engineering perturbative string duals for symmetric product orbifold CFTs,JHEP06(2024) 071, [arXiv:2312.05317]

    2024 arXiv

  42. [49]

    Sriprachyakul,Superstrings near the conformal boundary of AdS 3,JHEP08(2024) 203, [arXiv:2405.03678]

    V. Sriprachyakul,Superstrings near the conformal boundary of AdS 3,JHEP08(2024) 203, [arXiv:2405.03678]

    2024 arXiv

  43. [51]

    Dabholkar and A

    A. Dabholkar and A. Pakman,Exact chiral ring of AdS(3) / CFT(2),Adv. Theor. Math. Phys.13(2009), no. 2 409–462, [hep-th/0703022]

    2009 arXiv

  44. [52]

    Ferreira, M

    K. Ferreira, M. R. Gaberdiel, and J. I. Jottar,Higher spins on AdS 3 from the worldsheet, JHEP07(2017) 131, [arXiv:1704.08667]

    2017 arXiv

  45. [53]

    Giribet, A

    G. Giribet, A. Pakman, and L. Rastelli,Spectral Flow in AdS(3)/CFT(2),JHEP06(2008) 013, [arXiv:0712.3046]

    2008 arXiv

  46. [54]

    Iguri, N

    S. Iguri, N. Kovensky, and J. H. Toro,Spectral flow and string correlators in AdS 3×S 3×T 4, JHEP2023(2023) 161, [arXiv:2211.02521]

    2023 arXiv

  47. [55]

    Teschner,On structure constants and fusion rules in the SL(2,C) / SU(2) WZNW model, Nucl

    J. Teschner,On structure constants and fusion rules in the SL(2,C) / SU(2) WZNW model, Nucl. Phys. B546(1999) 390–422, [hep-th/9712256]

    1999 arXiv

  48. [56]

    Lunin and S

    O. Lunin and S. D. Mathur,Correlation functions for M**N / S(N) orbifolds,Commun. Math. Phys.219(2001) 399–442, [hep-th/0006196]

    2001 arXiv

  49. [57]

    Lunin and S

    O. Lunin and S. D. Mathur,Three point functions for M(N) / S(N) orbifolds with N=4 supersymmetry,Commun. Math. Phys.227(2002) 385–419, [hep-th/0103169]

    2002 arXiv

  50. [58]

    Dei and L

    A. Dei and L. Eberhardt,Correlators of the symmetric product orbifold,JHEP01(2020) 108, [arXiv:1911.08485]

    2020 arXiv

  51. [59]

    Lunin and S

    O. Lunin and S. D. Mathur,AdS / CFT duality and the black hole information paradox, Nucl. Phys. B623(2002) 342–394, [hep-th/0109154]

    2002 arXiv

  52. [60]

    M. R. Gaberdiel and B. Nairz,BPS correlators for AdS 3/CFT2,JHEP09(2022) 244, [arXiv:2207.03956]. – 54 –

    2022 arXiv

  53. [61]

    Eberhardt and M

    L. Eberhardt and M. R. Gaberdiel,String theory on AdS 3 and the symmetric orbifold of Liouville theory,Nucl. Phys. B948(2019) 114774, [arXiv:1903.00421]

    2019 arXiv

  54. [62]

    M. R. Gaberdiel, C. Peng, and I. G. Zadeh,Higgsing the stringy higher spin symmetry, JHEP10(2015) 101, [arXiv:1506.02045]

    2015 arXiv

  55. [63]

    Apolo, A

    L. Apolo, A. Belin, S. Bintanja, A. Castro, and C. A. Keller,Deforming symmetric product orbifolds: a tale of moduli and higher spin currents,JHEP08(2022) 159, [arXiv:2204.07590]

    2022 arXiv

  56. [64]

    M. R. Gaberdiel, R. Gopakumar, and B. Nairz,Beyond the tensionless limit: integrability in the symmetric orbifold,JHEP06(2024) 030, [arXiv:2312.13288]

    2024 arXiv

  57. [65]

    Roumpedakis,Comments on the S N orbifold CFT in the largeN-limit,JHEP07(2018) 038, [arXiv:1804.03207]

    K. Roumpedakis,Comments on the S N orbifold CFT in the largeN-limit,JHEP07(2018) 038, [arXiv:1804.03207]

    2018 arXiv

  58. [66]

    Giveon and M

    A. Giveon and M. Rocek,Supersymmetric string vacua on AdS(3) x N,JHEP04(1999) 019, [hep-th/9904024]

    1999 arXiv

  59. [67]

    Berenstein and R

    D. Berenstein and R. G. Leigh,Space-time supersymmetry in AdS(3) backgrounds,Phys. Lett. B458(1999) 297–303, [hep-th/9904040]

    1999 arXiv

  60. [68]

    Giveon and A

    A. Giveon and A. Pakman,More on superstrings in AdS(3) x N,JHEP03(2003) 056, [hep-th/0302217]

    2003 arXiv

  61. [69]

    Klemm and M

    A. Klemm and M. G. Schmidt,Orbifolds by Cyclic Permutations of Tensor Product Conformal Field Theories,Phys. Lett. B245(1990) 53–58

    1990

  62. [70]

    Fuchs, A

    J. Fuchs, A. Klemm, and M. G. Schmidt,Orbifolds by cyclic permutations in Gepner type superstrings and in the corresponding Calabi-Yau manifolds,Annals Phys.214(1992) 221–257

    1992

  63. [71]

    M. R. Gaberdiel and V. Sriprachyakul,Tensionless strings on AdS 3×S 3×S 3×S 1,JHEP05 (2025) 003, [arXiv:2411.16848]

    2025 arXiv

  64. [72]

    Baggio, M

    M. Baggio, M. R. Gaberdiel, and C. Peng,Higher spins in the symmetric orbifold of K3, Phys. Rev. D92(2015) 026007, [arXiv:1504.00926]

    2015 arXiv

  65. [73]

    Eguchi and Y

    T. Eguchi and Y. Sugawara,Duality in N=4 Liouville Theory and Moonshine Phenomena, PTEP2016(2016), no. 6 063B02, [arXiv:1603.02903]

    2016 arXiv

  66. [74]

    J. R. David, G. Mandal, and S. R. Wadia,Microscopic formulation of black holes in string theory,Phys. Rept.369(2002) 549–686, [hep-th/0203048]. – 55 –

    2002 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.