q -Poincaré invariance of the AdS3/CFT2

Riccardo Borsato

¹

,

Joakim Strömwall

²

,

Алессандро Торриелли

³

Abstract

We consider the exact R-matrix of AdS 3 /CFT 2 , which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds AdS 3 × S 3 × T 4 and AdS 3 × S 3 × S 3 × S 1 with pure Ramond-Ramond fluxes. We show that R is invariant under a "deformed boost" symmetry, for which we write an explicit exact coproduct, i.e. its action on two-particle states. When we include the boost, the symmetries of the R-matrix close into a q-Poincaré superalgebra. Our findings suggest that the recently discovered boost invariance in AdS 5 /CFT 4 may be a common feature of AdS/CFT systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the AdS 3 /CFT 2 classical r-matrix.

Boost generator in AdS3 integrable superstrings for general braiding

“…In previous articles [61,63,64] a coproduct was found which, although perfectly legitimate from an algebraic standpoint, annihilate the R-matrix. What we find here is more akin to what [62] studied for massive representations: these coproducts quasi-cocommute with the correspondent R-matrix in their family. In this sense they are a true symmetry of the correspondent R-matrix, as opposed to generating a differential equations of the type [1 st order diff.…”

“…This question was addressed in the context of the scattering problem in AdS 5 ×S 5 in [58,59] and revisited more recently in [60]. 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].…”

“…Due to their origin, we expect that similar ambiguities in the definition of the coproduct of the boost exist for the massive case. Thus, we plan to revisit the analysis performed in [62] from this new perspective.…”

Geometry of massless scattering in integrable superstring

“…In this paper, we have studied whether the R-matrix governing massless non-relativistic scatterings in AdS 2 ×S 2 ×T 6 is invariant under the action of the q-deformed Poincaré superalgebra in d = 2. Despite the behaviour of the boost action on the massless and massive R-matrices in the context of other integrable AdS backgrounds [71,72,74,75], we found that the R-matrix is neither invariant nor annihilated by the boost action. Nevertheless, we found that a linear combination of the boost coproduct and its opposite annihilates the R-matrix.…”

“…This will be brought to full fruition in this paper and potentially realises the sought-for connection with more traditional relativistic massless scattering. Another related approach was followed in [74,75].…”