$q$-Poincar\'e invariance of the $AdS_3/CFT_2$ $R$-matrix

TL;DR

This paper demonstrates that the $R$-matrix in $AdS_3/CFT_2$ exhibits $q$-Poincaré invariance through a deformed boost symmetry, suggesting a universal feature of integrable $AdS/CFT$ systems and proposing a universal classical $r$-matrix.

Contribution

The authors identify a deformed boost symmetry in the $AdS_3/CFT_2$ $R$-matrix and show it forms a $q$-Poincaré superalgebra, advancing the understanding of symmetries in integrable models.

Findings

$R$-matrix is invariant under a deformed boost symmetry.

The symmetry algebra closes into a $q$-Poincaré superalgebra.

Proposed a universal classical $r$-matrix for $AdS_3/CFT_2$.

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 $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^3 \times S^3 \times S^1$ 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 2-particle states. When we include the boost, the symmetries of the $R$-matrix close into a $q$-Poincar\'e 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.