Pith. sign in

REVIEW 3 major objections 3 minor 53 references

Thermodynamics of integrable N=2 theories, squared

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The squared N=2 integrable model has massive-sector UV central charge $c=6(1-1/k)$, not twice the earlier N=2 value.

desk verdict Useful TBA derivation, but the headline UV central charge rests on an inconsistent constant solution and is not proven. read the letter →

arxiv 2502.10356 v3 pith:RLADEH73 submitted 2025-02-14 hep-th

Xavier Kervyn , Davide Polvara , Alessandro Sfondrini This is my paper
classification hep-th
keywords ThermodynamicBetheansatzY-systemAdS3/CFT2mixedfluxrelativisticintegrablemodelsupersymmetricfieldtheorycentralchargeparafermions
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 works out the thermodynamics of a relativistic integrable field theory built by squaring an earlier N=2 theory: its S-matrix is a tensor product of two copies, giving twice as many supercharges but the same momentum-carrying particles. From the Bethe–Yang equations it derives a string hypothesis, TBA equations, and a Y-system that decouples into massive, massless-chiral, and massless-antichiral sectors. In the massive sector the ultraviolet central charge is claimed to be $c=6(1-1/k)$, which for $k\ge3$ is realized as a free $c=4$ theory plus $Z_{k-2}$ parafermions with $c=2-6/k$. In the massless sector the central charge is $c=N_0+2$, where $N_0$ — the number of massless momentum-carrying modes — is not fixed by the Bethe equations and must be input from outside (semiclassical comparisons favor $N_0=1$, giving $c=3$). The paper's central point is that doubling the supersymmetry does not double the ultraviolet central charge: interactions added by the tensor product make it smaller than twice the earlier N=2 result.

What carries the argument

The machine is the Y-system obtained from the TBA by acting with the right-inverse of the Cauchy kernel $s_k$. The massive Y-system is a finite-difference system for $Y_P$ ($P=1,\ldots,k-1$) plus two auxiliary functions; because the model is built as a tensor square, the number of auxiliary roots is doubled ($Z_{\alpha}=2$) relative to the earlier N=2 model. At twist $\mu=\pi$ and $L\to 0$ the physical constant solution has $Y_1=Y_{k-1}=Y_{\uparrow}=Y_{\downarrow}=0$, leaving the $A_{k-3}$ minimal Y-system, and the dilogarithm trick converts that solution into the ultraviolet central charge.

What would settle it

Run a numerical finite-volume solution of the TBA for $k=3$ at the twist value $\mu=\pi$, extract the ultraviolet central charge from $E(L)\simeq -\pi c/(6L)$, and compare the result with the two options $c=7$ ($N_0=1$) and $c=8$ ($N_0=2$).

Watch

Extended reading notes

Core claim

The paper claims that the finite-temperature and finite-volume properties of the mixed-flux relativistic model are governed by three decoupled TBA sectors. At twist $\mu=\pi$, the constant solutions of the massive Y-system force $Y_1=Y_{k-1}=Y_{\uparrow}=Y_{\downarrow}=0$; the remaining Y-functions satisfy the $A_{k-3}$ minimal-model Y-system, giving central charge $c=6(1-1/k)$ via the dilogarithm trick. For $k=2$ this gives $c=3$; for $k\ge3$ the UV limit splits into a free $c=4$ sector and $Z_{k-2}$ parafermions with $c=2-6/k$. The massless chiral/antichiral sector gives $c=N_0+2$, so the total UV central charge is conditional on $N_0$. The paper stresses that this central charge is not twice that of the earlier N=2 model; it is smaller.

Load-bearing premise

The value of $N_0$, the number of massless momentum-carrying modes, is not fixed by the Bethe equations; the massless central charge $c=N_0+2$ depends linearly on it, and the paper leans on external semiclassical comparisons (which favor $N_0=1$) to fix it.

Editorial extensions

If this is right

  • At $k=2$ the massive-sector result $c=3$ reproduces the previously known free-field content (two massive bosons and two massive fermions), providing a consistency check.
  • For $k\ge3$ the massive UV theory is described by a free $c=4$ sector plus $Z_{k-2}$ parafermions with $c=2-6/k$; if $N_0=1$, the massless sector adds a further free $c=3$.
  • The total UV central charge is not twice the earlier N=2 model's value: for the massive sector $c=6(1-1/k) < 6(k-1)/(k+1)$.
  • The massive Y-system with $Z_{\alpha}=1$ is periodic and yields the known conformal dimension of the perturbing operator, while for $Z_{\alpha}=2$ the system is not periodic and its remaining functions converge to a $2\pi i$-periodic $A_{k-3}$ solution.

Reading between the lines

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

  • If semiclassical input fixes $N_0=1$, the full UV central charge for $k\ge3$ is $c=9-6/k$ (massive $6(1-1/k)$ plus massless $3$); a numerical finite-$L$ TBA solution could test this directly.
  • The apparent non-supersymmetric split (a free $c=4$ sector plus $Z_{k-2}$ parafermions) suggests the UV limit may not be a superconformal fixed point; checking the superconformal algebra action on the UV spectrum would clarify whether the two copies of N=2 enhance or break conformal symmetry.
  • The same 'squaring' construction applied to the three-sphere variant of the background would give a one-parameter family of doubled N=2 theories; their TBA should be obtainable by the same $Z_{\alpha}=2$ Y-system and would interpolate between the results reported here.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper derives the finite-volume and finite-temperature thermodynamics of the relativistic integrable N=(2,2)"squared" (FPS) model of Frolov--Polvara--Sfondrini, obtained as the relativistic limit of mixed-flux AdS3 x S3 x T4 superstrings. Starting from the string Bethe--Yang equations, the authors take the h->0 limit, formulate a string hypothesis, derive TBA equations in the massive, massless-chiral and massless-antichiral sectors, simplify them to a Y-system (§3.6 and Appendix E), and solve the constant UV plateau at twist mu = pi to extract central charges: c = 6(1 - 1/k) for the massive sector (eq. 4.11), c = N_0 + 2 for the massless sectors (eq. 4.17, with N_0 left free), and the headline comparison c < 2 c_FI. The Z_alpha = 1 limit reproduces the Fendley--Intriligator results (eq. 4.7), and k = 2 gives c = 3 (eq. 4.15).

Significance. The TBA construction itself is competent and unusually transparent: the string-hypothesis step, the kernel identities, and the Y-system simplification are documented in detail (Appendices B--E), the FI (Z_alpha = 1) limit and the k = 2 limit reproduce known results, and the observation that doubling the supersymmetry does not double the central charge is a genuinely interesting claim. The authors are also commendably explicit about what they do not know: the number N_0 of massless modes is left free and the UV decoupling of Y_1, Y_{k-1} and the auxiliary Y-functions is flagged as lacking a first-principle explanation. If the massive-sector central-charge claim survived scrutiny, the paper would be a valuable contribution. At present, however, the central massive-sector result rests on an algebraic step that does not close, as detailed in the major comments; until that is repaired, c = 6(1 - 1/k) should be regarded as a conjecture supported mainly by the k = 2 case.

major comments (3)
  1. [§4, Eqs. (4.2), (4.8), (4.11)] The claimed constant solution (4.8) does not satisfy the massive Y-system (4.2) at mu = pi. For P = 1, the incidence matrix I_{P a} = delta_{P,1}delta_{a,up} + delta_{P,k-1}delta_{a,down} gives I_{1,up} = 1 and I_{1,down} = 0, so the equation reads Y_1^2 = (1 + Y_2)(1 + Y_0)(1 + 1/Y_up)^{Z_alpha}. Substituting (4.8), which sets Y_1 = 0 and Y_up = 0, the left-hand side is 0 while the right-hand side is (1 + Y_2) times an infinite factor (Y_2 is positive for k > 3 and zero but irrelevant for k = 3). The P = k - 1 equation has the analogous singularity with 1/Y_down. Thus (4.8) is not a solution of (4.2); it is the result of discarding the P = 1 and P = k - 1 equations after declaring Y_1 = Y_{k-1} = 0, i.e. a truncation to the interior A_{k-3} subsystem plus an assumed free sector. This is load-bearing: the central charge (4.11) is computed from (4.8) via the dilogarithm trick (4.6), whose derivation in Appendix D assumes regular plateau values with 0 < Y < infinity, and no regularization of the Y -> 0, 1/Y -> infinity limit is supplied. The statement in Section 4.1 that the authors lack a first-principle explanation for the decoupling is honest but does not repair the algebra: as written, eq. (4.8) is inconsistent with eq. (4.2), so the derivation of c = 6(1 - 1/k) for k >= 3 is currently invalid.
  2. [§4.1 and footnote 11] The uniqueness claim ("the only physical solution to the Y system (4.2) corresponds to (4.8)") is contradicted for k = 3. In that case the symmetric ansatz Y_1 = Y_2 = x, Y_up = Y_down = x/(1 + x) reduces (4.2) to x^4 = (1 + x)(1 + 2x)^2, which has a positive root x ~ 5.6, giving a genuine constant solution of (4.2) with all Y-functions positive and finite. The paper gives no selection criterion that excludes this solution apart from an undefined notion of "physical" ("real energy" is insufficient, since the free-energy integrals (4.6) are real for this solution). The footnote's "checked for a few values of k" is not documented and, in view of this counterexample, cannot amount to algebraic uniqueness. The authors should either list the constant solutions of (4.2) and prove that the TBA flow selects only the desired one, or present (4.8) and the resulting c = 6(1 - 1/k) explicitly as a conjecture. This is a second load-bearing gap in the central claim, independent of the algebraic inconsistency raised in the preceding comment.
  3. [§3.2 and Eq. (4.17)] The massless central charge c = N_0 + 2 depends linearly on N_0, and the manuscript states that this number is not fixed by the Bethe equations: "from the Bethe equations it seems this number should be N_0 = 2 comparisons with semiclassical results seem to suggest this number is actually N_0 = 1 [37]" (Section 3.2). Since the massless modes are an integral part of the model, any total central-charge statement for the full FPS theory is conditional on this external input. The authors are transparent about this, but it is load-bearing for the massless sector and for the comparison with FI: the abstract's "compute the UV central charge" overstates what is determined. The massless-sector result should be stated as N_0 + 2 with N_0 a parameter to be fixed by an independent computation, and the conclusions should not present a single total central charge without this caveat.
minor comments (3)
  1. [Eq. (3.49), first line] Both Y-functions on the left-hand side are printed with the same shift, Y_0^{(±)}(theta + i pi/2) Y_0^{(±)}(theta + i pi/2); crossing for massless particles, eq. (3.48), and comparison with the massive-system simplification (3.47) indicate the second factor should be evaluated at theta - i pi/2. Please correct this typo, since it obscures the derivation of the constant solution (4.3).
  2. [Throughout] Several typographical slips should be cleaned up: "arbitray" (Introduction), "relativisitic" (§2.5), "N◦ referstothenumberofindices ˙αandwhilefromtheBetheequations..." (Section 3.2, missing punctuation), and "where ours result agree with theirs" (Section 4.1). None of these affect the physics.
  3. [Abstract and conclusions] Given that N_0 is left free and the massive-sector decoupling is unproven, the abstract's unconditional phrasing ("compute the UV central charge", "the UV central charge of this model is not twice that of FI") should be qualified so that the reader immediately knows which parts of the result are established and which are conditional on the Y-system decoupling and on N_0.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the TBA/Y-system derivation is self-contained given the external S-matrix; the few overlapping self-citations enter as explicit inputs or unresolved ambiguities, not as load-bearing reductions.

full rationale

The derivation chain is: Bethe-Yang equations (2.56)-(2.61) to thermodynamic densities (3.18)-(3.21) to TBA equations (3.35)-(3.36) to Y-system (3.46)-(3.49) to constant solutions at mu=pi and the dilogarithm central-charge extraction in Section 4. Each step is a standard algebraic or thermodynamic manipulation with the kernels and identities stated in the paper; no parameter is fitted to the central charge and then renamed as a prediction. The central massive-sector value c=6(1-1/k) is obtained from the stated constant solution of the Y-system and the known Ak-3/parafermion result, not from an input that already contains this value. The only self-citations with overlapping authorship are [24] (the FPS S-matrix, an independently constructed input) and [37] (the semiclassical comparison suggesting N0=1). The paper explicitly leaves N0 free ('Here we will leave this number free', Section 3.2) and presents c=N0+2 as a conditional formula, so the massless sector is not a fitted-input-called-prediction. Two non-circular gaps are flagged by the paper itself: the UV decoupling of Y1, Yk-1, Y_up, Y_down 'is far less obvious' and 'We do not have a first-principle explanation for this decoupling' (Section 4.1), and the value of N0 is an external input. Whether the constant solution (4.8) literally satisfies (4.2) at the vanishing nodes is a mathematical-consistency question rather than a circularity: it does not make the target central charge equivalent to its own input by construction.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new particles or forces are introduced; the model and S-matrix are taken from [24]. The free-parameter list contains only N_0; the central results use the physical chemical-potential parameter mu=pi and the fixed Z_alpha=2 auxiliary-root count.

free parameters (1)
  • N_0 (number of massless momentum-carrying modes) = left free; semiclassical suggests 1, Bethe equations suggest 2
    The massless TBA equations (3.20) make the central charge c=N_0+2 depend linearly on N_0, which is not fixed by the Bethe equations. Section 3.2 leaves it free, citing semiclassical results [37] for N_0=1.
assumptions (5)
  • domain assumption The FPS S-matrix of [24], including minimal and CDD dressing factors, is the correct relativistic-limit S-matrix of mixed-flux AdS3 superstrings.
    Entire TBA input; Sections 2.2-2.4 quote [24] and take its dressing factors as given.
  • domain assumption The string hypothesis: only real auxiliary rapidities and those shifted by i pi survive in the thermodynamic limit; no other Bethe strings exist.
    Section 2.5 argues using |Y| bounds and the absence of massless bound states, but completeness is assumed, as standard in TBA.
  • domain assumption Massive, chiral and antichiral sectors decouple completely, so the free energy is the sum of three independent TBA systems.
    Section 2.4 notes S-matrix elements trivialize between sectors; used to write F = F_m + F_+ + F_- in (3.28).
  • standard math The dilogarithm trick and constant-Y-solution method give the UV central charge.
    Appendix D reviews Zamolodchikov's argument; assumes standard TBA-to-CFT dictionary.
  • ad hoc to paper The Y-system has a unique physical constant solution at mu=pi of the symmetric form (4.4).
    Section 4.1: 'We expect this system to have only one physical solution... we have checked that this holds for a few values of k.' No proof for all k.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Thermodynamics of integrable N=2 theories, squared." pith.science (2026). https://pith.science/paper/RLADEH73

@misc{pith2026250210356,
  author       = {Pith},
  title        = {Pith review of: Thermodynamics of integrable N=2 theories, squared},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLADEH73}},
  note         = {Machine review of arXiv:2502.10356}
}
abstract

In arXiv:2306.17553 a new supersymmetric integrable QFT was constructed from the relativistic limit of the worlsdheet theory of AdS$_3 \times$ S$^3\times $T$^4$ superstrings with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The model is closely reminiscent of one previously considered by Fendley and Intriligator, though it enjoys twice as many supersymmetries. In this paper we study its finite-volume and finite-temperature properties. We formulate the string hypothesis for the Bethe--Yang equations, write down the thermodynamic Bethe ansatz equations, and simplify them in the form of a Y-system. We obtain three decoupled sectors associated with massive, massless-chiral and massless-antichiral particles, for which we compute the UV central charge. We illustrate the similarities and differences between this model and the one of Fendley and Intriligator.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

53 extracted references · 14 canonical work pages

  1. [40]

    Exact results for the low energy AdS(4)XCP(3) string theory

    A. Fabbri, D. Fioravanti, S. Piscaglia and R. Tateo, Exact results for the low energyAdS4 x CP3 string theory, JHEP 11 (2013) 073 [ 1308.1861]

    work page Pith review arXiv 2013

  2. [38]

    Bombardelli, B

    D. Bombardelli, B. Stefański and A. Torrielli, The low-energy limit of AdS3/CFT2 and its TBA, JHEP 10 (2018) 177 [ 1807.07775]

    arXiv 2018

  3. [37]

    Frolov, A

    S. Frolov, A. Pribytok and A. Sfondrini, Ground state energy of twistedAdS3 × S3 × T 4 superstring and the TBA, 2305.17128

    arXiv

  4. [1]

    Maldacena, The large N limit of superconformal field theories and supergravity, Adv

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

    arXiv 1998

  5. [2]

    Lunin and J.M

    O. Lunin and J.M. Maldacena, Deforming field theories with U(1) x U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [ hep-th/0502086]

    arXiv 2005

  6. [3]

    Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201]

    S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201]

    arXiv 2005

  7. [4]

    Alday, G

    L.F. Alday, G. Arutyunov and S. Frolov, Green-Schwarz strings in TsT-transformed backgrounds, JHEP 0606 (2006) 018 [ hep-th/0512253]

    arXiv 2006

  8. [5]

    Ohlsson Sax and B

    O. Ohlsson Sax and B. Stefański, Closed strings and moduli in AdS3/CFT2, JHEP 05 (2018) 101 [ 1804.02023]

    arXiv 2018

Show all 53 references
  1. [6]

    Seibold and A

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

  2. [7]

    Cagnazzo and K

    A. Cagnazzo and K. Zarembo, B-field in AdS3/CFT2 correspondence and integrability, JHEP 1211 (2012) 133 [ 1209.4049]

    2012 arXiv

  3. [8]

    Beisert, C

    N. Beisert, C. Ahn, L.F. Alday, Z. Bajnok, J.M. Drummond, L. Freyhult et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys.99 (2012) 3 [ 1012.3982]

    2012 arXiv

  4. [9]

    Arutyunov and S

    G. Arutyunov and S. Frolov, Foundations of the AdS5 ×S5 superstring. part I, J. Phys. A A42 (2009) 254003 [ 0901.4937]. – 41 –

    2009 arXiv

  5. [10]

    Maldacena and H

    J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, R) WZW model. I, J. Math. Phys. 42 (2001) 2929 [ hep-th/0001053]

    2001 arXiv

  6. [11]

    Dei and A

    A. Dei and A. Sfondrini, Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 ×S3 ×S3 ×S1 WZW model, JHEP 02 (2019) 072 [ 1812.08195]

    2019 arXiv

  7. [12]

    M. Cho, S. Collier and X. Yin, Strings in Ramond-Ramond Backgrounds from the Neveu-Schwarz-Ramond Formalism, JHEP 12 (2020) 123 [ 1811.00032]

    2020 arXiv

  8. [13]

    Frolov and A

    S. Frolov and A. Sfondrini, New dressing factors for AdS3/CFT2, JHEP 04 (2022) 162 [2112.08896]

    2022 arXiv

  9. [14]

    Frolov and A

    S. Frolov and A. Sfondrini, Massless S matrices for AdS3/CFT2, JHEP 04 (2022) 067 [2112.08895]

    2022 arXiv

  10. [15]

    Frolov and A

    S. Frolov and A. Sfondrini, Mirror thermodynamic Bethe ansatz for AdS3/CFT2, JHEP 03 (2022) 138 [ 2112.08898]

    2022 arXiv

  11. [16]

    Ekhammar and D

    S. Ekhammar and D. Volin, Monodromy bootstrap for SU(2|2) quantum spectral curves: from Hubbard model to AdS3/CFT2, JHEP 03 (2022) 192 [ 2109.06164]

    2022 arXiv

  12. [17]

    Cavaglià, N

    A. Cavaglià, N. Gromov, B. Stefański, Jr. and A. Torrielli, Quantum Spectral Curve for AdS3/CFT2: a proposal, JHEP 12 (2021) 048 [ 2109.05500]

    2021 arXiv

  13. [18]

    Cavaglià, S

    A. Cavaglià, S. Ekhammar, N. Gromov and P. Ryan, Exploring the Quantum Spectral Curve for AdS3/CFT2, 2211.07810

    arXiv

  14. [19]

    Hoare, A

    B. Hoare, A. Stepanchuk and A. Tseytlin, Giant magnon solution and dispersion relation in string theory in AdS3 ×S3 ×T4 with mixed flux, Nucl. Phys. B879 (2014) 318 [ 1311.1794]

    2014 arXiv

  15. [20]

    Lloyd, O

    T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański, jr., The complete worldsheet S matrix of superstrings on AdS3 ×S3 ×T4 with mixed three-form flux, Nucl. Phys. B891 (2015) 570 [ 1410.0866]

    2015 arXiv

  16. [21]

    Frolov, D

    S. Frolov, D. Polvara and A. Sfondrini, Dressing Factors for Mixed-FluxAdS3 × S3 × T 4 Superstrings, 2402.11732

    arXiv

  17. [22]

    Frolov, D

    S. Frolov, D. Polvara and A. Sfondrini, Massive dressing factors for mixed-flux AdS3/CFT2, 2501.05995

    arXiv

  18. [23]

    Ohlsson Sax, D

    O. Ohlsson Sax, D. Riabchenko and B. Stefański, Worldsheet kinematics, dressing factors and odd crossing in mixed-flux AdS3 backgrounds, 2312.09288

    arXiv

  19. [24]

    Frolov, D

    S. Frolov, D. Polvara and A. Sfondrini, On mixed-flux worldsheet scattering in AdS3/CFT2, 2306.17553

    arXiv

  20. [25]

    Torrielli, A study of form factors in relativistic mixed-flux AdS3, JHEP 03 (2024) 082 [2312.17557]

    A. Torrielli, A study of form factors in relativistic mixed-flux AdS3, JHEP 03 (2024) 082 [2312.17557]

    2024 arXiv

  21. [26]

    Fendley and K.A

    P. Fendley and K.A. Intriligator, Scattering and thermodynamics of fractionally charged supersymmetric solitons, Nucl. Phys. B 372 (1992) 533 [ hep-th/9111014]

    1992 arXiv

  22. [27]

    Fendley and K.A

    P. Fendley and K.A. Intriligator, Scattering and thermodynamics in integrable N=2 theories, Nucl. Phys. B 380 (1992) 265 [ hep-th/9202011]

    1992 arXiv

  23. [28]

    Seibold and A

    F.K. Seibold and A. Sfondrini, Transfer matrices for AdS3/CFT2, JHEP 05 (2022) 089 [2202.11058]

    2022 arXiv

  24. [29]

    Arutyunov and S

    G. Arutyunov and S. Frolov, On string S-matrix, bound states and TBA, JHEP 0712 (2007) 024 [ 0710.1568]. – 42 –

    2007 arXiv

  25. [30]

    Borsato, O

    R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, jr., Towards the all-loop worldsheet S matrix for AdS3 ×S3 ×T4, Phys. Rev. Lett.113 (2014) 131601 [ 1403.4543]

    2014 arXiv

  26. [31]

    Borsato, O

    R. Borsato, O. Ohlsson Sax and A. Sfondrini, All-loop Bethe ansatz equations for AdS3/CFT2, JHEP 1304 (2013) 116 [ 1212.0505]

    2013 arXiv

  27. [32]

    Beisert, The su(2|2) dynamic S-matrix, Adv

    N. Beisert, The su(2|2) dynamic S-matrix, Adv. Theor. Math. Phys.12 (2008) 945 [hep-th/0511082]

    2008 arXiv

  28. [33]

    Arutyunov, S

    G. Arutyunov, S. Frolov, J. Plefka and M. Zamaklar, The off-shell symmetry algebra of the light-cone AdS5 ×S5 superstring, J. Phys. A40 (2007) 3583 [ hep-th/0609157]

    2007 arXiv

  29. [34]

    Sfondrini, Towards integrability for AdS3/CFT2, J

    A. Sfondrini, Towards integrability for AdS3/CFT2, J. Phys. A48 (2015) 023001 [ 1406.2971]

    2015 arXiv

  30. [35]

    Castillejo, R.H

    L. Castillejo, R.H. Dalitz and F.J. Dyson, Low’s scattering equation for the charged and neutral scalar theories, Phys. Rev. 101 (1956) 453

    1956

  31. [36]

    Braden, E

    H.W. Braden, E. Corrigan, P.E. Dorey and R. Sasaki, Affine Toda Field Theory and Exact S Matrices, Nucl. Phys. B 338 (1990) 689

    1990

  32. [39]

    Frolov and R

    S. Frolov and R. Suzuki, Temperature quantization from the TBA equations, Phys. Lett. B 679 (2009) 60 [ 0906.0499]

    2009 arXiv

  33. [41]

    Frolov, D

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

    arXiv

  34. [42]

    Ravanini, R

    F. Ravanini, R. Tateo and A. Valleriani, Dynkin TBAs, Int. J. Mod. Phys. A8 (1993) 1707 [hep-th/9207040]

    1993 arXiv

  35. [43]

    Klassen and E

    T.R. Klassen and E. Melzer, Purely Elastic Scattering Theories and their Ultraviolet Limits, Nucl. Phys. B 338 (1990) 485

    1990

  36. [44]

    Fateev and A.B

    V.A. Fateev and A.B. Zamolodchikov, Parafermionic Currents in the Two-Dimensional Conformal Quantum Field Theory and Selfdual Critical Points in Z(n) Invariant Statistical Systems, Sov. Phys. JETP 62 (1985) 215

    1985

  37. [45]

    Fiset and M.R

    M.-A. Fiset and M.R. Gaberdiel, Deformed Shatashvili-Vafa algebra for superstrings on AdS3 × M 7, JHEP 05 (2021) 156 [ 2101.10327]

    2021 arXiv

  38. [46]

    de la Ossa, M

    X. de la Ossa, M. Galdeano and E. Marchetto, SW-algebras and strings with torsion, 2412.13904

    arXiv

  39. [47]

    Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys

    A.B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B253 (1991) 391

    1991

  40. [48]

    Fontanella, O

    A. Fontanella, O. Ohlsson Sax, B. Stefański and A. Torrielli, The effectiveness of relativistic invariance in AdS3, JHEP 07 (2019) 105 [ 1905.00757]

    2019 arXiv

  41. [49]

    Janik, Review of AdS/CFT integrability, Chapter III.5: Lüscher corrections, Lett

    R.A. Janik, Review of AdS/CFT integrability, Chapter III.5: Lüscher corrections, Lett. Math. Phys. 99 (2010) 277 [ 1012.3994]. – 43 –

    2010 arXiv

  42. [50]

    Borsato, O

    R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, jr., The AdS3 ×S3 ×S3 ×S1 worldsheet S matrix, J. Phys. A48 (2015) 415401 [ 1506.00218]

    2015 arXiv

  43. [51]

    Seibold and A

    F.K. Seibold and A. Sfondrini, Interpolating families of integrable AdS3 backgrounds, 2502.07103

    arXiv

  44. [52]

    van Tongeren, Integrability of the AdS5 × S5 superstring and its deformations, J

    S.J. van Tongeren, Integrability of the AdS5 × S5 superstring and its deformations, J. Phys. A47 (2014) 433001 [ 1310.4854]

    2014 arXiv

  45. [53]

    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. – 44 –

    1990

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.