Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model

Abstract

We compute the tree-level bosonic S matrix in light-cone gauge for superstrings on pure-NSNS AdS 3 ×S 3 ×S 3 ×S 1. We show that it is proportional to the identity and that it takes the same form as for AdS 3 × S 3 × T 4 and for flat space. Based on this, we make a conjecture for the exact worldsheet S matrix and derive the mirror thermodynamic Bethe ansatz (TBA) equations describing the spectrum. Despite a non-trivial vacuum energy, they can be solved in closed form and coincide with a simple set of Bethe ansatz equations-again much like AdS 3 × S 3 × T 4 and flat space. This suggests that the model may have an integrable spin-chain interpretation. Finally, as a check of our proposal, we compute the spectrum from the worldsheet CFT in the case of highest-weight representations of the underlying Kač-Moody algebras, and show that the mirror-TBA prediction matches it on the nose.

TT¯ deformations as TsT transformations

“…This property is well-known in the context light-cone gauge-fixed strings [35], and has also been verified perturbatively for a number of models, see e.g. [27,59,60].…”

“…21 This is because in this case p1ω(p2) − p2ω(p1) = ±2p1p2, nor does it vanish for same-chirality scattering-a fact that is crucial in order to reproduce the spectrally-flowed sectors of the WZW description, see refs. [25,27].…”

“…Interesting applications to several classes of two-dimensional theories, such as supersymmetric theories[11][12][13][14][15], 2-d gravity[16][17][18][19] and AdS3/CFT2 holography[20][21][22][23][24][25][26][27][28][29], also emerged.…”

TT¯ deformations with N=(0,2Jiang1, Sfondrini2, Tartaglino‐Mazzucchelli3 2019Phys. Rev. D576770View full textAdd to dashboardCite

“…Interestingly, the "TT " CDD factor had also appeared in the study of the S matrix on the worldsheet of flat-space strings [3,[11][12][13][14][15][16], strongly suggesting that flat-space strings are the TT deformation of a free theory (a fact that can also be substantiated from a Lagrangian or Hamiltonian analysis [3,15,16]). Indeed TT deformations are naturally related [15,16] to the "uniform" light-cone gauge which is quite natural for the study of integrable strings theories [17][18][19], and the TT CDD factor also describes the scattering on more general backgrounds such as AdS 3 Wess-Zumino-Witten backgrounds [15,20,21]. 2 A separate, but equally interesting link between TT deformations and AdS 3 strings appears in the context of holography [27][28][29][30][31][32][33][34], where the deformed two-dimensional theory is the holographic dual of some (AdS 3 ) gravity or string theory, rather than being a worldsheet theory.…”

Gravitational perturbations as TT¯-deformations in 2D dilaton gravity systems

“…It is also interesting to try to relax our condition so as to support non-conformal matter fields, more general types of dilaton potential, and general forms of dilaton coupling to matter fields. In particular, it has been shown that Yang-Baxter deformations [24][25][26] are closely related to TT -deformations [27,28] (For related works, see [29,30] as well). Hence…”