$q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix

Abstract

We consider the exact $R$-matrix of $Ad{S}_3/CF{T}_2$, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds $Ad{S}_3\times S^3\times T^4$ and $Ad{S}_3\times S^3\times S^3\times S^1$ 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 $q$-Poincaré superalgebra. Our findings suggest that the recently discovered boost invariance in $Ad{S}_5/CF{T}_4$ 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 $Ad{S}_3/CF{T}_2$ classical $r$-matrix.

26 pages. Minor improvements and references added. Published version

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• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
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