Pith. sign in

REVIEW 2 major objections 7 minor 2 cited by

Interpolating families of integrable AdS3 backgrounds

T0 review · 2 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read This paper constructs families of integrable string backgrounds that interpolate between the AdS3 x S3 x S3 x S1 background and geometries with two-spheres in place of one or both three-spheres, preserving half the supersymmetry.

desk verdict Genuinely new interpolating families of integrable AdS3 backgrounds, with explicit data and a solid pp-wave check; the main question for a referee is whether the mixed-flux formulas satisfy the supergravity equations. read the letter →

arxiv 2502.07103 v3 pith:WSM55UHI submitted 2025-02-10 hep-th

Fiona K. Seibold , Alessandro Sfondrini This is my paper · ORCID
classification hep-th
keywords AdS3/CFT2integrabledeformationsTsTtransformationsS3superstringspp-wavelimitDrinfel'd-Reshetikhintwistd(21alpha)superalgebraRRandNSNSflux
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

This paper claims that the $AdS_3 \times S^3 \times S^3 \times S^1$ superstring background admits TsT deformations that interpolate continuously to either $AdS_3 \times S^3 \times S^2 \times T^2$ or $AdS_3 \times S^2 \times S^2 \times T^3$, and that the same construction interpolates between $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^2 \times T^5$. These deformed backgrounds preserve half of the original supersymmetry, namely one copy of the $\mathfrak{d}(2,1;\alpha)$ superalgebra, or one copy of $\mathfrak{psu}(1,1|2)$ in the contracted cases. Because the deformation is a TsT transformation, integrability is preserved and the effect on the worldsheet S matrix is a Drinfel'd-Reshetikhin twist, which makes the deformed models amenable to the standard integrability formalism in the full quantum theory. The authors provide explicit supergravity data, identify 1/8-BPS geodesics, and compute pp-wave metrics and quadratic Hamiltonians with dispersion relations, giving a concrete starting point for quantising these backgrounds.

What carries the argument

The central machinery is the TsT transformation: T-duality along one $U(1)$ isometry, a shift along a second $U(1)$ isometry, and T-duality back, applied to the Hopf-fibre coordinates $\xi_1, \xi_2$ of the two three-spheres and the coordinate $x$ on the $S^1$ factor. The deformations are expressed through the squashed-sphere metric $ds^2(S^3_{j,\Delta}) = \tfrac14(ds^2(S^2_j) + \Delta A_j^2)$, where $A_j = d\xi_j - \cos\theta_j\, d\eta_j$, with $\Delta$ the deformation parameter. The TsT transformation preserves integrability by acting as a Drinfel'd-Reshetikhin twist on the worldsheet S matrix, and this theorem is what lets the paper claim full quantum integrability from the pp-wave data alone. In the pp-wave limit the same machinery yields explicit quadratic Hamiltonians whose diagonalisation gives the dispersion relations quoted in the text.

What would settle it

Take the explicit metric, B-field, dilaton and RR fluxes of Section 4 for generic $q$ and $\Delta$ and verify the full set of type IIB supergravity equations of motion; if they fail for any $0<q<1$ with $0<\Delta<1$, the interpolation is not a genuine string background. A second direct check is to compute the exact lightcone S matrix at finite $\Delta$ and see whether it differs from the undeformed one by a $\Delta$-dependent factor beyond a constant phase, which would contradict the Drinfel'd-Reshetikhin twist picture.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the known integrable backgrounds listed in its Table 1 are connected by families of integrable deformations: starting from $AdS_3 \times S^3 \times S^3 \times S^1$ and TsT-transforming pairs of the $U(1)$ isometries associated with the Hopf fibres of the two three-spheres and the $S^1$ circle, one obtains a one-parameter or, in general, three-parameter family of type IIB supergravity solutions that still preserve one copy of $\mathfrak{d}(2,1;\alpha)$. In the strong-deformation limit with pure-RR flux, the squashed three-spheres become two-spheres and the families reach $AdS_3 \times S^3 \times S^2 \times T^2$ or $AdS_3 \times S^2 \times S^2 \times T^3$, up to the global topology of the tori; taking $\alpha$ to $0$ or $1$ gives the interpolation between $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^2 \times T^5$ with $\mathfrak{psu}(1,1|2)$ preserved. The paper also computes the pp-wave limit around suitable 1/8-BPS geodesics and diagonalises the resulting quadratic Hamiltonians. The dispersion relations of the deformed models differ from those of the undeformed background only by constant R-charge shifts attributed to the different lightcone gauge choice, matching the expected behaviour of a TsT twist.

Load-bearing premise

The load-bearing premise is that a TsT transformation always maps a valid supergravity background to another valid background while preserving integrability, so the deformed models inherit both the classical and quantum integrability of the undeformed $AdS_3 \times S^3 \times S^3 \times S^1$ string; the paper invokes this theorem from the literature rather than proving it for these specific backgrounds.

Editorial extensions

If this is right

  • One can move continuously from the maximally supersymmetric $AdS_3 \times S^3 \times S^3 \times S^1$ string to the lower-symmetry $AdS_3 \times S^3 \times S^2 \times T^2$ and $AdS_3 \times S^2 \times S^2 \times T^3$ strings without losing integrability or more than half of the supersymmetry.
  • The $\alpha \to 0$ and $\alpha \to 1$ contractions turn this into integrable interpolations from $AdS_3 \times S^3 \times T^4$ to $AdS_3 \times S^2 \times T^5$ preserving a $\mathfrak{psu}(1,1|2)$ superalgebra.
  • The deformation parameter $\Delta$ does not appear in the pp-wave dispersion relations, only constant R-charge shifts do, so the deformed models should be exactly solvable by the same worldsheet S matrix as the undeformed background with twisted boundary conditions.
  • For mixed-flux starting points the strong-deformation limit only squashes the sphere down to a finite radius controlled by $q$, while the pure-RR case is the one that reaches the genuine $S^2$ geometry; this distinguishes which endpoints are actually connected by the interpolation.
  • The explicit backgrounds provide concrete targets for the integrability construction of spectra on the $AdS_3 \times S^2 \times M$ backgrounds, which currently lack the same machinery as the $S^3$-based ones.

Reading between the lines

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

  • A natural next step the authors do not take is to compute the full worldsheet S matrix of the deformed models at finite $\Delta$ and check explicitly that it coincides with the undeformed S matrix up to a Drinfel'd-Reshetikhin twist; the pp-wave results strongly suggest this, but the quantum check is not carried out here.
  • If the interpolation extends to the elliptic deformations mentioned in Section 7, the same geometry could host quantum-group symmetries rather than ordinary twists, which would make the spectrum qualitatively different despite the identical squashed metric.
  • The obstruction for $q>0$ may indicate that the mixed-flux moduli space has a boundary or a phase transition between the RR endpoint and the squashed family; probing the lightcone spectrum across $q$ could reveal where the twist description breaks down.
  • The interpolation offers a possible route to define string theory on $AdS_3 \times S^2 \times M$ by analytic continuation from the better-understood $AdS_3 \times S^3 \times S^3 \times S^1$ models, in the spirit of how $\alpha \to 0$ limits relate the $T^4$ and $S^3 \times S^3$ families.
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

2 major / 7 minor

Summary. The paper constructs TsT deformations of the AdS3×S3×S3×S1 type IIB string background. Two one-parameter families are presented explicitly (metric, B-field, and RR fluxes): a TsT in (ξ2, x) that in the strong-deformation limit reaches AdS3×S3×S2×T2 (Section 4), and a TsT in (ξ1, ξ2) that reaches AdS3×S2×S2×T3 (Section 5). A three-parameter family (Section 6) contains both as special cases. The authors argue that the deformed backgrounds preserve one copy of d(2,1;α), i.e., half of the supersymmetry of the original background, and that they inherit integrability from the TsT construction. For each family they identify a geodesic satisfying the left-BPS condition, take the pp-wave limit, and compute the quadratic light-cone Hamiltonian and the dispersion relations, which are independent of the deformation parameters. The pure-RR endpoints are claimed to match the known backgrounds (2.6)–(2.7); for mixed flux q>0 the strong-deformation limit leaves a squashed sphere, so the endpoint is not reached.

Significance. Should the explicit backgrounds pass a direct supergravity check, the paper delivers a systematic construction of previously unknown interpolating families between the maximally supersymmetric AdS3×S3×S3×S1 background and the lower-supersymmetry AdS3×S3×S2×T2 and AdS3×S2×S2×T3 backgrounds, with all supergravity fields written out. The TsT construction makes the inheritance of classical integrability transparent and ties the deformation to a Drinfel'd-Reshetikhin twist picture. The pp-wave analysis is a genuine output rather than an input: the Δ-independence of the dispersion relations in (4.72), (5.40), and (6.19) is a nontrivial consistency check of that picture, and the comparison with trigonometric deformations in Section 7 exhibits parameter-dependent dispersion relations in the non-TsT case. The three-parameter deformation is a useful completeness result for the class of left-supersymmetry-preserving TsT deformations, and the authors are candid that the full quantum integrable analysis is not performed. The main risk is the absence of an explicit verification of the supergravity equations for the mixed-flux fields.

major comments (2)
  1. [§4.1, Eqs. (4.11)–(4.16) and §5.1, Eqs. (5.5)–(5.7)] The explicit mixed-flux fields are the central output of the paper, but the paper does not verify that they satisfy the type IIB equations of motion and Bianchi identities, nor does it spell out why the field redefinition (4.12) (and the analogous step in Section 5) preserves the solution property after the TsT chain. The TsT theorem cited from [20–22] guarantees that the intermediate fields are a solution, but the presented H3, F3, F5 are the fields after a nontrivial linear redefinition of coordinates; an error in the pullback or in the flux expressions would invalidate the backgrounds. Please provide a direct check (for instance, a computer-algebra verification of the IIB equations and Bianchi identities at generic Δ and q) or a careful step-by-step argument that the redefinition is a diffeomorphism transforming the fluxes in the standard way. This is load-bearing because the paper's central claim is that the interpolating families are string backgrounds.
  2. [§4.1, Eqs. (4.5)–(4.9) and §5.1, Eqs. (5.8)–(5.12)] The strong-deformation limit is claimed to reproduce 'precisely' the known endpoint backgrounds (2.6) and (2.7), but the coefficient matching is not shown. After the rescaling (4.5) the limiting S2 has radius R2/2, since the squashed-sphere metric (3.6) reduces to (R2²/4)ds²(S²) at Δ→0, and the flux coefficients in (4.7)–(4.9) must be matched against (2.6) using the case-2 radius relations in (2.3); this comparison is not transparent because the notation in (2.6)–(2.7) does not make clear which radius multiplies each volume form. The same comment applies to the AdS3×S2×S2×T3 endpoint in Section 5. Please display the matching of the metric, H3, F3, and F5 coefficients explicitly.
minor comments (7)
  1. [§4.4, Eq. (4.70)] The term '− αq(x3 ´x4 − x3 ´x4)' is a typo and should presumably read '− αq(x3 ´x4 − x4 ´x3)'.
  2. [§6.4, Eq. (6.17)] The terms 'γ2(1 − α)(x5 ´x8 − x5 ´x3)' and '(x3 ´x6 − ´x3x6)' contain typos; they should read 'γ2(1 − α)(x5 ´x8 − x8 ´x5)' and '(x3 ´x6 − x6 ´x3)', respectively.
  3. [§2 and §4.1, Eqs. (2.6)–(2.7) and (4.6)–(4.9)] The notation for the flux coefficients is ambiguous about which radius (R, R1, or R2, and whether before or after the rescaling) multiplies each volume form; please define the normalization of Ω(S²) and state the radius of the limiting S² explicitly.
  4. [§4.4, before Eq. (4.68)] The word 'ligthcone' should be 'lightcone'.
  5. [§4.2, after Eq. (4.34)] When stating that there is no non-trivial real solution, please specify that the trivial solution J1 = J2 = 0 is the one being excluded.
  6. [§4.1, after Eq. (4.13)] It would be helpful to state explicitly that for q > 0 the strong-deformation endpoint is a squashed three-sphere with Δ = q², not an S², since this is a key physical conclusion of the mixed-flux analysis.
  7. [§4.4, Eq. (4.70)] The signs of the B-field coupling terms (for example −q(x1 ´x2 − x2 ´x1)) appear opposite to those obtained by substituting (4.62) into (4.69) with the standard convention; the dispersion relations are insensitive to the overall sign, but please check and state the sign convention used.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the interpolating backgrounds are forward TsT transforms of known AdS3 solutions, with integrability imported from an external theorem; dispersion relations are outputs, not inputs.

full rationale

The construction is a forward computation. Section 3 invokes the TsT theorem via citations [20-22] (Lunin-Maldacena; Frolov; Alday-Arutyunov-Frolov), none of which is authored by the present authors, so the integrability-preservation and solution-mapping properties are external support rather than self-citation. The explicit backgrounds (4.10)-(4.16), (5.2)-(5.7), and (6.4)-(6.5) are obtained by writing down TsT transforms of the known AdS3 x S3 x S3 x S1 solution (2.4), with no parameter fitted to the claimed endpoints; the strong-deformation limits are compared to the known backgrounds (2.6)-(2.7). The pp-wave Hamiltonians and dispersion relations are computed from the deformed data, and the observed independence of the deformation parameter Delta is presented as a consistency check of the TsT-twist picture, not as an input assumption. Self-citations such as [14], [15], [37], and [42] are contextual or explanatory and are not load-bearing for the central claim. The paper's own caveat that no fully-fledged quantum integrability analysis was performed, and the skeptic's observation that the mixed-flux fields are not explicitly substituted into the IIB supergravity equations, are limitations or correctness risks, not circular reductions.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No genuinely new entities are introduced. The deformation parameters are continuous family parameters, not fitted constants. The construction relies on established TsT and classification theorems, which are cited.

free parameters (4)
  • TsT deformation parameter delta (or s)
    Continuous parameter of the TsT shift, eqs. (4.1), (4.12), (5.1), (6.1)-(6.3). It is chosen by hand to define the family of backgrounds and is not fitted to data. For mixed flux, it ranges q^2 <= delta <= 1.
  • Parameter alpha
    The d(2,1;alpha) parameter of the original AdS3×S3×S3×S1 background, eq. (1.1). Input of the undeformed theory, not fitted.
  • Flux parameter q
    Relative strength of NSNS vs RR flux, satisfying q^2 + qhat^2 = 1, eq. (2.5). Input of the undeformed theory.
  • Three-parameter deformation parameters delta'_1, delta'_2, delta (or gamma_1, gamma_2)
    Parameters of the most general TsT deformation in Section 6 and Appendix A, eqs. (A.1)-(A.4). They continuously parametrize the family.
assumptions (5)
  • domain assumption TsT transformations preserve integrability of the string sigma model and act on the worldsheet S matrix as a Drinfel'd-Reshetikhin twist.
    Invoked in Section 3 to conclude that the TsT-deformed backgrounds are integrable. Cited to [20-23]; the paper does not reprove this.
  • domain assumption TsT transformations map type II supergravity solutions to type II supergravity solutions.
    Used implicitly in Sections 4-6 to claim the constructed metrics and fluxes are consistent supergravity backgrounds. This is a standard property of T-duality and shift.
  • domain assumption The classification of all symmetric-space type IIB backgrounds with an AdS3 factor, as summarized in Table 1, is complete.
    Used in Section 2 to identify the endpoints of the interpolations (cases 1, 2, 3, 4, 5) and to state that the strong-deformation limit reproduces known backgrounds. Cited to [34,35].
  • domain assumption The BPS bound of the d(2,1;alpha) algebra is L0 = alpha J1 + (1-alpha) J2 (and barred analog).
    Used in Sections 4.2 and 5.2 to select the 1/8-BPS geodesic for the pp-wave limit. This is a known property of the superalgebra, used without proof.
  • standard math The light-cone gauge-fixed quadratic Hamiltonian and the form of the dispersion relations are computed using standard pp-wave techniques.
    The derivations in Sections 4.4, 5.4, 6.4 follow the standard Virasoro constraint method; no new axioms beyond ordinary physics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Interpolating families of integrable AdS3 backgrounds." pith.science (2026). https://pith.science/paper/WSM55UHI

@misc{pith2026250207103,
  author       = {Pith},
  title        = {Pith review of: Interpolating families of integrable AdS3 backgrounds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WSM55UHI}},
  note         = {Machine review of arXiv:2502.07103}
}
abstract

We construct families of integrable deformations that interpolate between $AdS_3\times S^3\times S^3\times S^1$ and either $AdS_3\times S^3\times S^2\times T^2$ or $AdS_3\times S^2\times S^2\times T^3$. They preserve half of the supersymmetry of the original background, namely one copy of the $\mathfrak{d}(2,1;\alpha)$ algebra. From this it follows a similar integrable interpolation between $AdS_3\times S^3\times T^4$ and $AdS_3\times S^2\times T^5$, which also preserves half of the supersymmetry, namely a copy of the $\mathfrak{psu}(1,1|2)$ algebra. In all cases, the interpolating backgrounds are constructed by using TsT transformations, which makes it easy to implement them in the integrability formalism in the full quantum theory. To illustrate this point, we discuss the lightcone gauge fixing of the models and compute their pp-wave Hamiltonian.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Tree-level S matrix for $\lambda$-deformed AdS3 strings

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    For the λ-deformed AdS3×S3×T4 superstring, the tree-level bosonic worldsheet S matrix is purely elastic for 0≤λ<1, confirming integrability, and ill-defined at λ→1, so that limit does not capture T-dual worldsheet dynamics.

  2. Thermodynamics of integrable N=2 theories, squared

    hep-th 2025-02 conditional novelty 6.0 of 10

    The FPS model's massive sector has UV central charge c=6(1-1/k), its massless sectors contribute c=N_0+2, so doubling the supersymmetry does not double the central charge.

Reference graph

Works this paper leans on

43 extracted references · 9 canonical work pages · cited by 2 Pith papers

  1. [1]

    Maldacena, The Large N limit of superconformal field theories and superg ravity, Adv

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

    arXiv 1998

  2. [2]

    Arutyunov and S

    G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S5 Superstring. Part I , J. Phys. A 42 (2009) 254003 [0901.4937]

    arXiv 2009

  3. [3]

    Beisert et al., Review of AdS/CFT Integrability: An Overview , Lett

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

    arXiv 2012

  4. [4]

    Cagnazzo and K

    A. Cagnazzo and K. Zarembo, B-field in AdS(3)/CFT(2) Correspondence and Integrability , JHEP 11 (2012) 133 [1209.4049]

    arXiv 2012

  5. [5]

    Sfondrini, Towards integrability for AdS3/ CFT2, J

    A. Sfondrini, Towards integrability for AdS3/ CFT2, J. Phys. A 48 (2015) 023001 [1406.2971]

    arXiv 2015

  6. [6]

    Demulder, S

    S. Demulder, S. Driezen, B. Knighton, G. Oling, A.L. Reto re, F.K. Seibold et al., Exact approaches on the string worldsheet , J. Phys. A 57 (2024) 423001 [2312.12930]

    arXiv 2024

  7. [7]

    Ekhammar and D

    S. Ekhammar and D. Volin, Monodromy bootstrap for SU (2|2) quantum spectral curves: from Hubbard model to AdS 3/CFT2, JHEP 03 (2022) 192 [2109.06164]

    arXiv 2022

  8. [8]

    Cavagli` a, N

    A. Cavagli` a, N. Gromov, B. Stefa´ nski, Jr., Jr. and A. To rrielli, Quantum Spectral Curve for AdS3/CFT2: a proposal , JHEP 12 (2021) 048 [2109.05500]

    arXiv 2021

Show all 43 references
  1. [9]

    Frolov and A

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

    2022 arXiv

  2. [10]

    Brollo, D

    A. Brollo, D. le Plat, A. Sfondrini and R. Suzuki, Tensionless Limit of Pure–Ramond-Ramond Strings and AdS3/CFT2 , Phys. Rev. Lett. 131 (2023) 161604 [2303.02120]

    2023 arXiv

  3. [11]

    Ohlsson Sax and B

    O. Ohlsson Sax and B. Stefa´ nski, Closed strings and moduli in AdS 3/CFT2, JHEP 05 (2018) 101 [1804.02023]

    2018 arXiv

  4. [12]

    Babichenko, B

    A. Babichenko, B. Stefanski, Jr. and K. Zarembo, Integrability and the AdS(3)/CFT(2) correspondence , JHEP 03 (2010) 058 [0912.1723]

    2010 arXiv

  5. [13]

    Hoare, Integrable deformations of sigma models , J

    B. Hoare, Integrable deformations of sigma models , J. Phys. A 55 (2022) 093001 [2109.14284]. – 25 –

    2022 arXiv

  6. [14]

    Seibold and A

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

  7. [15]

    Hoare, F.K

    B. Hoare, F.K. Seibold and A.A. Tseytlin, Integrable supersymmetric deformations of AdS 3× S3× T4, JHEP 09 (2022) 018 [2206.12347]

    2022 arXiv

  8. [16]

    Orlando and L.I

    D. Orlando and L.I. Uruchurtu, Warped anti-de Sitter spaces from brane intersections in ty pe II string theory, JHEP 06 (2010) 049 [1003.0712]

    2010 arXiv

  9. [17]

    Orlando, S

    D. Orlando, S. Reffert and L.I. Uruchurtu, Classical Integrability of the Squashed Three-sphere, War ped AdS3 and Schroedinger Spacetime via T-Duality , J. Phys. A 44 (2011) 115401 [1011.1771]

    2011 arXiv

  10. [18]

    Orlando and L.I

    D. Orlando and L.I. Uruchurtu, Integrable Superstrings on the Squashed Three-sphere , JHEP 10 (2012) 007 [1208.3680]

    2012 arXiv

  11. [19]

    Israel, C

    D. Israel, C. Kounnas, D. Orlando and P.M. Petropoulos, Electric/magnetic deformations of S**3 and AdS(3), and geometric cosets , Fortsch. Phys. 53 (2005) 73 [hep-th/0405213]

    2005 arXiv

  12. [20]

    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]

    2005 arXiv

  13. [21]

    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]

    2005 arXiv

  14. [22]

    Alday, G

    L.F. Alday, G. Arutyunov and S. Frolov, Green-Schwarz strings in TsT-transformed backgrounds , JHEP 06 (2006) 018 [hep-th/0512253]

    2006 arXiv

  15. [23]

    van Tongeren and Y

    S.J. van Tongeren and Y. Zimmermann, Do Drinfeld twists of AdS5 × S5 survive light-cone quantization?, SciPost Phys. Core 5 (2022) 028 [2112.10279]

    2022 arXiv

  16. [24]

    Itsios and K

    G. Itsios and K. Sfetsos, AdS solutions and λ -deformations, Nucl. Phys. B 953 (2020) 114960 [1911.12371]

    2020 arXiv

  17. [25]

    Itsios, Type-II backgrounds from deformed coset CFTs , 2411.11086

    G. Itsios, Type-II backgrounds from deformed coset CFTs , 2411.11086

    arXiv

  18. [26]

    Maldacena and H

    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]

    2001 arXiv

  19. [27]

    Baggio and A

    M. Baggio and A. Sfondrini, Strings on NS-NS Backgrounds as Integrable Deformations , Phys. Rev. D 98 (2018) 021902 [1804.01998]

    2018 arXiv

  20. [28]

    Dei and A

    A. Dei and A. Sfondrini, Integrable spin chain for stringy Wess-Zumino-Witten model s, JHEP 07 (2018) 109 [1806.00422]

    2018 arXiv

  21. [29]

    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

  22. [30]

    Borsato and L

    R. Borsato and L. Wulff, Marginal deformations of WZW models and the classical Yang–B axter equation, J. Phys. A 52 (2019) 225401 [1812.07287]

    2019 arXiv

  23. [31]

    Eloy and G

    C. Eloy and G. Larios, Charting the conformal manifold of holographic CFT 2’s, SciPost Phys. 17 (2024) 123 [2405.17542]

    2024 arXiv

  24. [32]

    Blau, J.M

    M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papado poulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [hep-th/0201081]

    2002 arXiv

  25. [33]

    Berenstein, J.M

    D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N=4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021]

    2002 arXiv

  26. [34]

    Wulff, All symmetric AdS n>2 solutions of type II supergravity , J

    L. Wulff, All symmetric AdS n>2 solutions of type II supergravity , J. Phys. A 50 (2017) 495402 [1706.02118]. – 26 –

    2017 arXiv

  27. [35]

    Wulff, Classifying integrable symmetric space strings via factor ized scattering, JHEP 02 (2018) 106 [1711.00296]

    L. Wulff, Classifying integrable symmetric space strings via factor ized scattering, JHEP 02 (2018) 106 [1711.00296]

    2018 arXiv

  28. [36]

    Borsato, O

    R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefa´ ns ki, The AdS3 × S3 × S3 × S1 worldsheet S matrix, J. Phys. A 48 (2015) 415401 [1506.00218]

    2015 arXiv

  29. [37]

    Borsato, S

    R. Borsato, S. Driezen, B. Hoare, A.L. Retore and F.K. Se ibold, Inequivalent light-cone gauge-fixings of strings on AdSn × Sn backgrounds, Phys. Rev. D 109 (2024) 106023 [2312.17056]

    2024 arXiv

  30. [38]

    Frolov, T T , ~J J, JT and ~JT deformations, J

    S. Frolov, T T , ~J J, JT and ~JT deformations, J. Phys. A 53 (2020) 025401 [1907.12117]

    2020 arXiv

  31. [39]

    Hoare, A.L

    B. Hoare, A.L. Retore and F.K. Seibold, Elliptic deformations of the AdS3 × S3 × T 4 string, JHEP 04 (2024) 042 [2312.14031]

    2024

  32. [40]

    Hoare, Towards a two-parameter q-deformation of AdS 3 × S3 × M 4 superstrings, Nucl

    B. Hoare, Towards a two-parameter q-deformation of AdS 3 × S3 × M 4 superstrings, Nucl. Phys. B 891 (2015) 259 [1411.1266]

    2015 arXiv

  33. [41]

    Seibold, Two-parameter integrable deformations of the AdS3 × S3 × T 4 superstring, JHEP 10 (2019) 049 [1907.05430]

    F.K. Seibold, Two-parameter integrable deformations of the AdS3 × S3 × T 4 superstring, JHEP 10 (2019) 049 [1907.05430]

    2019 arXiv

  34. [42]

    Frolov and A

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

    2022 arXiv

  35. [43]

    Witten, Instantons and the large N = 4 algebra, J

    E. Witten, Instantons and the large N = 4 algebra, J. Phys. A 58 (2025) 035403 [2407.20964]. – 27 –

    2025 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.