String Theory as a Higher Spin Theory

TL;DR

This paper demonstrates that string theory on a specific AdS background exhibits a higher spin symmetry, with the massive spectrum organized into representations of a Higher Spin Square, revealing a new algebraic structure in string theory.

Contribution

It introduces the Higher Spin Square (HSS) as the symmetry algebra organizing the string spectrum on AdS3, connecting string states to higher spin representations.

Findings

Massive string spectrum forms representations of the HSS.

Untwisted sector corresponds to multiparticle states of a minimal representation.

Twisted sector states relate to tensor products of larger, novel representations.

Abstract

The symmetries of string theory on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ at the dual of the symmetric product orbifold point are described by a so-called Higher Spin Square (HSS). We show that the massive string spectrum in this background organises itself in terms of representations of this HSS, just as the matter in a conventional higher spin theory does so in terms of representations of the higher spin algebra. In particular, the entire untwisted sector of the orbifold can be viewed as the Fock space built out of the multiparticle states of a single representation of the HSS, the so-called `minimal' representation. The states in the twisted sector can be described in terms of tensor products of a novel family of representations that are somewhat larger than the minimal one.