Abstract
We focus on the massless sector of the AdS3/CFT2 correspondence motivated by the pursuit of finding a complete spectrum of scattering on the worldsheet for generic values of the mass, to extend the previously known scattering spectrum in the massive sector.
Using integrability we find a deformed Poincaré superalgebra that is exactly realised on the worldsheet, a novel feature for this and the AdS2/CFT1 correspondence. This type of deformed algebra only becomes a partial symmetry in the trademark AdS5/CFT4 correspondence. In our case, the deformation affects the relativistic invariance and allows the deformed "near-relativistic" frames to become boosted. We find a representation of the generator of boosts and its coproduct and show that the coproduct exactly satisfes the homomorphism property.
First we find analytically a representation of a boost coproduct that is consistent only in the massless sector, then with the help of symbolic computer algebra we find a representation of a generalised coproduct that is valid in both the massive and the massless sectors.
In the semiclassical limit we rescale the boost and momentum generators to contract the deformed Poincaré algebra into a classical loop superalgebra, where we propose a classical universal r-matrix. Deforming the loop algebra, we find the universal form of the cobracket of all generators, including the boost.