Higher spin algebras and large $\mathcal{N}=4$ holography

TL;DR

This paper introduces a new family of higher spin algebras derived from matrix extensions of shs[lambda], identifies dual coset CFTs, and connects these theories to string theory on specific AdS3 backgrounds.

Contribution

It discovers a novel class of higher spin algebras, links them to coset CFTs, and relates these to string theory on particular AdS3  S3 backgrounds.

Findings

New higher spin algebras from matrix extensions of shs[lambda]

Identification of coset CFTs realizing these algebras

Connection to string theory on AdS3  S3  S3  backgrounds

Abstract

A new family of higher spin algebras that arises upon restricting matrix extensions of $\mathfrak{shs}[\lambda]$ is found. We identify coset CFTs realising these symmetry algebras, and thus propose new higher spin-CFT dual pairs. These higher spin theories arise naturally as a subsector of string theory on ${\rm AdS}_3\times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ for specific ratios of the radii of the two spheres.