AdS3/CFT2 and q-Poincare' superalgebras

TL;DR

This paper identifies a deformation of the 1+1D Poincare' superalgebra realized in the massless sector of AdS3/CFT2 integrable scattering, extending previous partial symmetries observed in higher-dimensional cases.

Contribution

It provides a complete representation of the deformed Poincare' superalgebra, including the boost operator and its coproduct, with a classical limit and potential physical analogies.

Findings

Deformed Poincare' superalgebra realized in AdS3/CFT2 massless sector

Explicit representation of boost operator and coproduct

Classical limit and analogy with phonons

Abstract

We discover that a certain deformation of the 1+1 dimensional Poincare' superalgebra is exactly realised in the massless sector of the AdS3/CFT2 integrable scattering problem. Deformed Poincar\'e superalgebras were previously noticed to appear in the AdS5/CFT4 correspondence - which displays only massive excitations -, but they were there only a partial symmetry. We obtain a representation of the boost operator and its coproduct, and show that the comultiplication exactly satisfies the homomorphism property. We present a classical limit, and finally speculate on an analogy with the physics of phonons.