The effectiveness of relativistic invariance in AdS3

Abstract

We use relativistic invariance to investigate two aspects of integrable AdS3 string theory. Firstly, we write down the all-loop TBA equations for the massless sector of the theory with R-R flux, using the recently discovered hidden relativistic symmetry. Secondly, for the low-energy relativistic limit of the theory with NS-NS flux we write down the S matrix, dressing factors and TBA. We find that the integrable system coincides with a restriction to AdS3 of the relativistic q-deformed AdS5 theory.We also comment on the relativistic limit of the small-k NS-NS theory. 1 andrea.fontanella@inv.uam.es 2 olof.ohlsson.sax@nordita.org 3 Bogdan.Stefanski.1@city.ac.uk 4 a.torrielli@surrey.ac.uk AcknowledgmentsWe very much thank Diego Bombardelli for discussions, collaboration on the initial stages of the project and continuing assistance. We very much thank Ben Hoare, Tim Hollowood and Arkady Tseytlin for reading the manuscript and for very useful comments and discussions. We thank Alessandra Cagnazzo,

Geometry of massless scattering in integrable superstring

“…It would be desirable to show in a purely analytic fashion, without relying on numerical computations, that the expression available in the literature [29] for the non-relativistic dressing phase does indeed only depend on the difference of the γ variables, and attains the precise Sine-Gordon form without the contribution from any CDD factors. Progress in this direction has recently been made in [30], where the property of being of difference form in the γ variables was derived purely analytically for the massless non-relativistic AdS 3 dressing phase constructed in [29], and the absence of CDD factors was motivated. This has shown that (2.15) is indeed satisfied exactly also by the dressing factor as well, and therefore no modifications to that equation occur as a consequence of introducing such factor.…”

Semiclassical quantization of the mixed-flux AdS3 giant magnon

“…Furthermore, massless modes render a perturbative computation of wrapping corrections impossible, once the theory is put on a compactified worldsheet 9 [87]. Instead, wrapping corrections may be computed from a non-perturbative TBA using an alternative low-momentum expansion [88][89][90].…”

Boost generator in AdS3 integrable superstrings for general braiding

“…We can also pose the same question in the context of the AdS 3 /CFT 2 correspondence, where it has already been studied in [61][62][63] for the AdS 3 ×S 3 ×T 4 background. In particular, in [64,65] a new variable was found which allows to recast the complete non-relativistic massless S-matrix (inclusive of the dressing factor) in a way which not only displays manifest difference form, but it also attains the exact same analytic expression as in the near (left-left and right-right moving) BMN limit [35]. In all cases a suitably modified Poincaré symmetry was found and boost operators were identified, although several proposals were made each with different defining features.…”

“…Here we will revisit the AdS 3 × S 3 × T 4 scattering problem from a new perspective and attempt to incorporate the different proposals within one and the same unifying framework. We will also investigate why the difference form achieved by [64,65] seems to be tied to a very specific choice of braiding factor in the coproduct. 1 In doing that we will discover an interesting and unexpected relation between certain ambiguities in the definition of the boost operator and the very structure of the R-matrix.…”