Integrability and the AdS
                     3/CFT
                     2 correspondence

Babichenko, A.; Stefański, Bogdan; Zarembo, Konstantin

doi:10.1007/jhep03(2010)058

Cited by 192 publications

(370 citation statements)

References 102 publications

(158 reference statements)

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“…19 There is an interesting open question about the possible relation between this exact S-matrix appearing in the q → 1 limit for scattering of "solitonic" states with the dispersion relation (4.3) and the massless S-matrices for scattering of elementary excitations in the k = 1 [30] and k > 1 [31] SU (2) WZW model. 20 In this sense, the case of AdS 3 × S 3 × S 3 × S 1 theory appears to be a more complicated 1-parameter generalization as there the symmetry algebra depends on the deformation parameter α [11,12].…”

Section: Discussionmentioning

confidence: 99%

“…The AdS 3 × S 3 × S 3 × S 1 supported just by RR flux (q = 0) depends on α ∈ (0, 1) [11,28,12] 22 so one may compare this one-parameter generalization of AdS 3 × S 3 × T 4 with the one (with NSNS flux parameter q) we discussed in this paper. One obvious difference is that the two theories have different 21 Here k stands for the coefficient in front of the action of the Pohlmeyer-reduced theory.…”

Section: Discussionmentioning

confidence: 99%

“…The presence of this additional automorphism, in principle, allows one to introduce different mass values (as is the case, e.g., for the AdS 3 × S 3 × S 3 × S 1 theory with pure RR flux [11]) through rescaling the eigenvalue of M.…”

Section: S-matrix In the Bmn Limitmentioning

confidence: 99%

“…Let us start by reviewing the pure RR case discussed in [5] (see also [11,26,12] for related earlier work). As was briefly discussed in section 3.1, for q = 0 there is a formal symmetry under the interchange of the two irreducible atypical representations.…”

Section: Q = 0 Casementioning

confidence: 99%

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Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Hoare¹,

Tseytlin²

2013

Nuclear Physics B

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The type IIB supergravity AdS 3 × S 3 × T 4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the treelevel S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q = 0 case in arXiv:1303.5995.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: S-matrix In the Bmn Limitmentioning

confidence: 99%

Section: Q = 0 Casementioning

confidence: 99%

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Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Hoare¹,

Tseytlin²

2013

Nuclear Physics B

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“…These theories are important as they are conjectured to be dual to some gauge theories [36]. They are classical integrable [33,37,38] 1 . Quantum integrability is tightly connected with Yangian symmetry at the quantum level.…”

Section: Introductionmentioning

confidence: 99%

Yangian superalgebras in conformal field theory

Creutzig

2011

Nuclear Physics B

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Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP N−1|N sigma models, while the former are conjecturally dual to supersphere sigma models. *

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AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

Eghbali

2024

Fortschritte der Physik

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The author proceed to construct a dual pair for the background by applying non‐Abelian T‐duality (here as Poisson–Lie [PL] T‐duality on a semi‐Abelian double). By using a certain parametrization of the 4‐dimensional Lie group and by a suitable choice of spectator‐dependent matrices the original ‐model including the metric and a non‐trivial ‐field are constructed. The dual background constructed by means of the PL T‐duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non‐trivial ‐flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non‐Abelian T‐dual ‐models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two‐loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

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Integrability and the AdS 3/CFT 2 correspondence

Cited by 192 publications

References 102 publications

Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Yangian superalgebras in conformal field theory

AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

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