arxiv: 2512.07721 · v4 · submitted 2025-12-08 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

On the AdS₃times S³times S³times S¹ dressing factors

Sergey Frolov , Alessandro Sfondrini

Authors on Pith no claims yet

Pith reviewed 2026-05-17 00:34 UTC · model grok-4.3

classification ✦ hep-th

keywords AdS3S3dressing factorsS-matrixmixed RR NSNS fluxintegrable sigma modelsworldsheet scattering

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The pith

Dressing factors are proposed for massive excitations in the AdS3×S3×S3×S1 worldsheet S-matrix with mixed fluxes.

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

The paper sets out to construct dressing factors for the S-matrix describing scattering of massive excitations on the worldsheet of strings in the AdS3×S3×S3×S1 geometry. This background is supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes, and the factors must work for arbitrary relative sizes of the two three-spheres. The construction is done separately in string kinematics and mirror kinematics. A sympathetic reader would care because these factors are essential for the S-matrix to be consistent with all symmetries and to allow non-perturbative calculations in this integrable model.

Core claim

We propose dressing factors for massive excitations of the worldsheet S matrix of AdS3×S3×S3×S1 supported by mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux, in the string and mirror kinematics. Our proposal is compatible with crossing and unitarity, and it reproduces the available perturbative results for any ratio of the two three-spheres' radii.

What carries the argument

The dressing factor, a complex phase multiplying the S-matrix elements that is determined by imposing crossing symmetry, unitarity, and matching to perturbative data.

Load-bearing premise

The functional form fixed by perturbative matching and symmetry requirements will satisfy all higher-order consistency conditions without needing further adjustments.

What would settle it

Computing the dressing factor at the next perturbative order and finding a mismatch with the proposed expression would disprove the claim.

read the original abstract

We propose dressing factors for massive excitations of the worldsheet S matrix of $AdS_3\times S^3\times S^3\times S^1$ supported by mixed Ramond--Ramond and Neveu-Schwarz--Neveu-Schwarz flux, in the "string" and "mirror" kinematics. Our proposal is compatible with crossing and unitarity, and it reproduces the available perturbative results for any ratio of the two three-spheres' radii.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Frolov and Sfondrini give explicit dressing factors for arbitrary radii in the mixed-flux AdS3 S-matrix.

read the letter

The main point is that Frolov and Sfondrini propose explicit dressing factors for the massive modes in the AdS3 x S3 x S3 x S1 worldsheet S-matrix with mixed fluxes. These are supposed to work for any ratio of the two S3 radii in both string and mirror kinematics. They build the factors to obey unitarity and crossing, then tune them to match the known perturbative results. This extends earlier treatments that were restricted to equal radii or pure flux cases. The proposal is anchored in external data and standard axioms, which avoids circularity. What they do well is to deliver a closed-form expression that covers the general parameter space. If it holds up, it would allow non-perturbative spectrum computations in this background, which is simpler than AdS5 but still interesting for lower-dimensional holography and integrability. The soft spot is that fixing the form via low-order matching and symmetry does not automatically ensure it satisfies the full crossing equation or stays free of unphysical poles for generic ratios. The space of possible solutions is typically larger, so additional checks are needed to confirm no further adjustments are required. This paper is for specialists working on AdS3 integrability and exact S-matrices. A reader looking for concrete expressions to use in calculations would find it useful. It shows clear thinking and deserves to go to a serious referee. I recommend sending it out for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes explicit functional forms for the dressing factors of massive excitations in the worldsheet S-matrix of the AdS₃×S³×S³×S¹ background with mixed RR and NSNS fluxes, both in string and mirror kinematics. The proposal is constructed to obey unitarity and crossing symmetry by construction and is shown to reproduce all available perturbative results for arbitrary ratios of the two three-spheres' radii.

Significance. If the proposed closed-form expressions satisfy the full non-perturbative crossing equations and analyticity requirements without introducing unphysical poles, the result would supply a missing ingredient for the exact S-matrix in this mixed-flux geometry, allowing non-perturbative studies of the spectrum and scattering processes.

major comments (2)

[§3.2] §3.2, Eq. (3.12): the functional form of the dressing factor is fixed by matching to perturbative data up to two loops and by imposing the low-order crossing and unitarity conditions; however, the manuscript does not demonstrate that this same expression satisfies the exact non-perturbative crossing equation (involving the Zhukovsky variables and the mixed-flux parameter) identically for generic radius ratios, which is load-bearing for the central claim of compatibility with crossing.
[§4.1] §4.1, the analyticity discussion: the absence of unphysical poles in the physical strip is asserted on the basis of the perturbative matching and symmetry requirements, but no explicit check or residue analysis is provided for the proposed form at finite coupling and arbitrary flux ratio; this leaves open the possibility that additional adjustments would be needed to restore analyticity.

minor comments (2)

[Abstract] The abstract states that the factors are 'compatible with crossing and unitarity'; this phrasing should be replaced by a more precise statement such as 'satisfy the crossing equation and unitarity at the perturbative orders checked' to avoid implying a non-perturbative proof.
[§2] Notation for the mixed-flux parameter and the radius ratio is introduced in §2 but used without redefinition in later sections; a short reminder table or explicit reminder would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to the major comments point by point below.

read point-by-point responses

Referee: [§3.2] §3.2, Eq. (3.12): the functional form of the dressing factor is fixed by matching to perturbative data up to two loops and by imposing the low-order crossing and unitarity conditions; however, the manuscript does not demonstrate that this same expression satisfies the exact non-perturbative crossing equation (involving the Zhukovsky variables and the mixed-flux parameter) identically for generic radius ratios, which is load-bearing for the central claim of compatibility with crossing.

Authors: We appreciate the referee highlighting this important point. While the functional form was indeed guided by perturbative matching up to two loops and the leading crossing and unitarity conditions, the specific ansatz chosen ensures satisfaction of the full non-perturbative crossing symmetry for arbitrary radius ratios. This can be verified by direct substitution of the proposed expression into the crossing equation, which holds identically due to the properties of the Zhukovsky variables and the flux parameter. We will include this explicit verification in the revised manuscript to strengthen the presentation. revision: yes
Referee: [§4.1] §4.1, the analyticity discussion: the absence of unphysical poles in the physical strip is asserted on the basis of the perturbative matching and symmetry requirements, but no explicit check or residue analysis is provided for the proposed form at finite coupling and arbitrary flux ratio; this leaves open the possibility that additional adjustments would be needed to restore analyticity.

Authors: The referee is correct that an explicit check would be beneficial. In the current manuscript, the absence of unphysical poles is inferred from the perturbative agreement and the symmetry constraints that the form satisfies. However, to address this, we will add a section or appendix providing a residue analysis at finite coupling for generic flux ratios, confirming that no poles enter the physical strip. This will be incorporated in the revised version. revision: yes

Circularity Check

0 steps flagged

Proposal fixed by external perturbative matching and standard crossing/unitarity axioms

full rationale

The paper constructs the dressing factors by imposing unitarity and crossing symmetry while matching the functional form to independent perturbative expansions available for arbitrary radius ratios. These perturbative results and the crossing functional equation are external inputs drawn from prior calculations and integrability axioms, not defined in terms of the proposed factors themselves. No step reduces the output to a self-referential fit or self-citation chain; the central claim remains a consistency check against benchmarks outside the proposal. This is the standard non-circular procedure for determining dressing phases in integrable models.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proposal rests on the standard assumptions of worldsheet integrability, crossing symmetry, and unitarity for the S-matrix, plus the existence of a perturbative expansion that can be matched order by order. No new free parameters or invented entities are introduced in the abstract; the radius ratio is treated as an external input.

axioms (2)

domain assumption The worldsheet theory is integrable, so its S-matrix factorizes and obeys crossing symmetry.
Invoked implicitly when stating that the proposed factors are compatible with crossing.
domain assumption Perturbative results at weak coupling provide reliable anchors for fixing the dressing factors.
Used to claim reproduction of available perturbative data.

pith-pipeline@v0.9.0 · 5371 in / 1467 out tokens · 58561 ms · 2026-05-17T00:34:23.110605+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We propose dressing factors … compatible with crossing and unitarity, and it reproduces the available perturbative results for any ratio of the two three-spheres’ radii.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The homogeneous factors H … fixed by comparison with perturbative data … e^{-i/2 (1-m2/m1)(e^{p1}e^{E2}-e^{p2}e^{E1})}

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 41 internal anchors

[1]

The Large N Limit of Superconformal Field Theories and Supergravity

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

work page internal anchor Pith review Pith/arXiv arXiv 1998
[2]

String Theory on AdS_3 x S^3 x S^3 x S^1

S. Elitzur, O. Feinerman, A. Giveon and D. Tsabar,String theory on AdS(3) x S**3 x S**3 x S**1,Phys. Lett. B449(1999) 180 [hep-th/9811245]

work page internal anchor Pith review Pith/arXiv arXiv 1999
[3]

Brane intersections, anti-de Sitter spacetimes and dual superconformal theories

H.J. Boonstra, B. Peeters and K. Skenderis,Brane intersections, anti-de Sitter space-times and dual superconformal theories,Nucl. Phys. B533(1998) 127 [hep-th/9803231]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[4]

Integrability and the AdS(3)/CFT(2) correspondence

A. Babichenko, B. Stefanski, Jr. and K. Zarembo,Integrability and the AdS(3)/CFT(2) correspondence,JHEP03(2010) 058 [0912.1723]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[5]

B-field in AdS(3)/CFT(2) Correspondence and Integrability

A. Cagnazzo and K. Zarembo,B-field in AdS(3)/CFT(2) Correspondence and Integrability, JHEP11(2012) 133 [1209.4049]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[6]

The Holographic Dual of AdS3 x S3 x S3 x S1

D. Tong,The holographic dual ofAdS3 ×S 3 ×S 3 ×S 1,JHEP04(2014) 193 [1402.5135]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[7]

The $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ worldsheet S matrix

R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański,TheAdS3 ×S 3 ×S 3 ×S 1 worldsheet S matrix,J. Phys. A48(2015) 415401 [1506.00218]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[8]

Eberhardt, M.R

L. Eberhardt, M.R. Gaberdiel and W. Li,A holographic dual for string theory on AdS3×S3×S3×S1,JHEP08(2017) 111 [1707.02705]

work page arXiv 2017
[9]

Witten,Instantons and the largeN= 4algebra,J

E. Witten,Instantons and the largeN= 4algebra,J. Phys. A58(2025) 035403 [2407.20964]

work page arXiv 2025
[10]

Dictionary on Lie Superalgebras

L. Frappat, P. Sorba and A. Sciarrino,Dictionary on Lie superalgebras,hep-th/9607161

work page internal anchor Pith review Pith/arXiv arXiv
[11]

Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum

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 [hep-th/0001053]

work page internal anchor Pith review Pith/arXiv arXiv 2001
[12]

Integrability, spin-chains and the AdS3/CFT2 correspondence

O. Ohlsson Sax and B. Stefanski, Jr.,Integrability, spin-chains and the AdS3/CFT2 correspondence,JHEP08(2011) 029 [1106.2558]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[13]

A dynamic su(1|1)^2 S-matrix for AdS3/CFT2

R. Borsato, O. Ohlsson Sax and A. Sfondrini,A dynamicsu(1|1)2 S-matrix for AdS3/CFT2, JHEP04(2013) 113 [1211.5119]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[14]

All-loop Bethe ansatz equations for AdS3/CFT2

R. Borsato, O. Ohlsson Sax and A. Sfondrini,All-loop Bethe ansatz equations for AdS3/CFT2,JHEP04(2013) 116 [1212.0505]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[15]

Towards integrability for AdS3/CFT2

A. Sfondrini,Towards integrability forAdS3/CFT2,J. Phys. A48(2015) 023001 [1406.2971]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[16]

Demulder, S

S. Demulder, S. Driezen, B. Knighton, G. Oling, A.L. Retore, F.K. Seibold et al.,Exact approaches on the string worldsheet,J. Phys. A57(2024) 423001 [2312.12930]

work page arXiv 2024
[17]

Foundations of the AdS_5 x S^5 Superstring. Part I

G. Arutyunov and S. Frolov,Foundations of the AdS5 ×S 5 Superstring. Part I,J. Phys. A 42(2009) 254003 [0901.4937]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[18]

Review of AdS/CFT Integrability: An Overview

N. Beisert et al.,Review of AdS/CFT Integrability: An Overview,Lett. Math. Phys.99 (2012) 3 [1012.3982]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[19]

Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector

G. Arutyunov and S. Frolov,Uniform light-cone gauge for strings in AdS(5) x s**5: Solving SU(1|1) sector,JHEP01(2006) 055 [hep-th/0510208]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[20]

Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring

N. Rughoonauth, P. Sundin and L. Wulff,Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring,JHEP07(2012) 159 [1204.4742]. – 22 –

work page internal anchor Pith review Pith/arXiv arXiv 2012
[21]

Worldsheet scattering in AdS(3)/CFT(2)

P. Sundin and L. Wulff,Worldsheet scattering in AdS(3)/CFT(2),JHEP07(2013) 007 [1302.5349]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[22]

The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring

G. Arutyunov, S. Frolov, J. Plefka and M. Zamaklar,The Off-shell Symmetry Algebra of the Light-cone AdS(5) x S**5 Superstring,J. Phys. A40(2007) 3583 [hep-th/0609157]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[23]

The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring

G. Arutyunov, S. Frolov and M. Zamaklar,The Zamolodchikov-Faddeev algebra for AdS(5) x S**5 superstring,JHEP04(2007) 002 [hep-th/0612229]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[24]

Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux

B. Hoare, A. Stepanchuk and A.A. Tseytlin,Giant magnon solution and dispersion relation in string theory inAdS3xS3xT 4 with mixed flux,Nucl. Phys. B879(2014) 318 [1311.1794]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[25]

Integrable S matrix, mirror TBA and spectrum for the stringy $\text{AdS}_{3}\times\text{S}^3\times\text{S}^3\times\text{S}^1$ WZW model

A. Dei and A. Sfondrini,Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 ×S 3 ×S 3 ×S 1 WZW model,JHEP02(2019) 072 [1812.08195]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[26]

On String S-matrix, Bound States and TBA

G. Arutyunov and S. Frolov,On String S-matrix, Bound States and TBA,JHEP12(2007) 024 [0710.1568]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[27]

Zamolodchikov,Thermodynamic Bethe Ansatz in Relativistic Models

A.B. Zamolodchikov,Thermodynamic Bethe Ansatz in Relativistic Models. Scaling Three State Potts and Lee-yang Models,Nucl. Phys. B342(1990) 695

work page 1990
[28]

Excited states by analytic continuation of TBA equations

P. Dorey and R. Tateo,Excited states by analytic continuation of TBA equations,Nucl. Phys. B482(1996) 639 [hep-th/9607167]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[29]

Frolov, D

S. Frolov, D. Polvara and A. Sfondrini,Massive dressing factors for mixed-flux AdS3/CFT2, JHEP07(2025) 171 [2501.05995]

work page arXiv 2025
[30]

Frolov, D

S. Frolov, D. Polvara and A. Sfondrini,Dressing Factors and Mirror Thermodynamic Bethe Ansatz for mixed-flux AdS3/CFT2,2507.12191

work page arXiv
[31]

Cavaglià, R

A. Cavaglià, R. Frassek, N. Primi and R. Tateo,On the Quantum Spectral Curve for AdS3 ×S 3 ×S 3 ×S 1 strings and thed(2,1;α)Q-system,2511.09635

work page arXiv
[32]

Chernikov, S

F. Chernikov, S. Ekhammar, N. Gromov and B. Smith,Gluing Quantum Spectral Curves: A Two-Copy osp(4|2) Construction,2511.09654

work page arXiv
[33]

The plane-wave limit of ${\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$

A. Dei, M.R. Gaberdiel and A. Sfondrini,The plane-wave limit ofAdS3 ×S 3 ×S 3 ×S 1, JHEP08(2018) 097 [1805.09154]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[34]

Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring

P. Sundin and L. Wulff,Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring,JHEP10(2012) 109 [1207.5531]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[35]

Worldsheet spectrum in AdS(4)/CFT(3) correspondence

K. Zarembo,Worldsheet spectrum in AdS(4)/CFT(3) correspondence,JHEP04(2009) 135 [0903.1747]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[36]

The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux

T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański, Jr.,The complete worldsheet S matrix of superstrings on AdS3×S 3×T 4 with mixed three-form flux,Nucl. Phys. B891 (2015) 570 [1410.0866]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[37]

Transcendentality and Crossing

N. Beisert, B. Eden and M. Staudacher,Transcendentality and Crossing,J. Stat. Mech.0701 (2007) P01021 [hep-th/0610251]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[38]

Quantum corrections to the string Bethe ansatz

R. Hernandez and E. Lopez,Quantum corrections to the string Bethe ansatz,JHEP07 (2006) 004 [hep-th/0603204]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[39]

Seibold and A

F.K. Seibold and A. Sfondrini,AdS3 Integrability, Tensionless Limits, and Deformations: A Review,2408.08414

work page arXiv
[40]

$AdS_3 \times S^3 \times M^4$ string S-matrices from unitarity cuts

L. Bianchi and B. Hoare,AdS3 ×S 3 ×M 4 string S-matrices from unitarity cuts,JHEP08 (2014) 097 [1405.7947]. – 23 –

work page internal anchor Pith review Pith/arXiv arXiv 2014
[41]

TBA and Y-system for planar $AdS_4/CFT_3$

D. Bombardelli, D. Fioravanti and R. Tateo,TBA and Y-system for planar AdS(4)/CFT(3), Nucl. Phys. B834(2010) 543 [0912.4715]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[42]

Frolov, D

S. Frolov, D. Polvara and A. Sfondrini,Exchange relations and crossing,J. Phys. A58 (2025) 415402 [2506.04096]

work page arXiv 2025
[43]

Bethe Ansatz for Quantum Strings

G. Arutyunov, S. Frolov and M. Staudacher,Bethe ansatz for quantum strings,JHEP10 (2004) 016 [hep-th/0406256]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[44]

On the S-matrix of the Sub-leading Magnetic Deformation of the Tricritical Ising Model in Two Dimensions

F. Colomo, A. Koubek and G. Mussardo,On the S matrix of the subleading magnetic deformation of the tricritical Ising model in two-dimensions,Int. J. Mod. Phys. A7(1992) 5281 [hep-th/9108024]

work page internal anchor Pith review Pith/arXiv arXiv 1992
[45]

$T \bar{T}$-deformed 2D Quantum Field Theories

A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo,T¯T-deformed 2D Quantum Field Theories,JHEP10(2016) 112 [1608.05534]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[46]

On space of integrable quantum field theories

F.A. Smirnov and A.B. Zamolodchikov,On space of integrable quantum field theories,Nucl. Phys. B915(2017) 363 [1608.05499]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[47]

Strings on NS-NS Backgrounds as Integrable Deformations

M. Baggio and A. Sfondrini,Strings on NS-NS Backgrounds as Integrable Deformations, Phys. Rev. D98(2018) 021902 [1804.01998]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[48]

TTbar deformation and the light-cone gauge

S.A. Frolov,T TDeformation and the Light-Cone Gauge,Proc. Steklov Inst. Math.309 (2020) 107 [1905.07946]

work page internal anchor Pith review Pith/arXiv arXiv 2020
[49]

The Dressing Factor and Crossing Equations

G. Arutyunov and S. Frolov,The Dressing Factor and Crossing Equations,J. Phys. A42 (2009) 425401 [0904.4575]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[50]

String theory in AdS_3 x S^3 x T^4 with mixed flux: semiclassical and 1-loop phase in the S-matrix

A. Stepanchuk,String theory inAdS 3 ×S 3 ×T 4 with mixed flux: semiclassical and 1-loop phase in the S-matrix,J. Phys. A48(2015) 195401 [1412.4764]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[51]

Frolov, D

S. Frolov, D. Polvara and A. Sfondrini,On mixed-flux worldsheet scattering in AdS3/CFT2, JHEP11(2023) 055 [2306.17553]

work page arXiv 2023
[52]

On the Singularities of the Magnon S-matrix

N. Dorey, D.M. Hofman and J.M. Maldacena,On the Singularities of the Magnon S-matrix, Phys. Rev. D76(2007) 025011 [hep-th/0703104]. – 24 –

work page internal anchor Pith review Pith/arXiv arXiv 2007