String Theory as a Higher Spin Theory

TL;DR

This work analyzes string theory on $AdS_3 \times S^3 \times \mathbb{T}^4$ at the symmetric product orbifold point through the lens of the Higher Spin Square (HSS), a stringy extension of higher spin symmetry built from a vertical hs$[1]$ algebra and a horizontal counterpart. It shows the entire untwisted sector is captured by the Fock space of the HSS minimal representation and its tensor powers, mirroring the perturbative sector of a Vasiliev-type higher spin theory based on the HSS. The twisted sector is described as representations larger than the minimal one, forming a one-parameter (and supersymmetric) family of level-one-like representations that yield Cardy-like growth, with a detailed analysis of the two-cycle case and BPS-state implications. Overall, the paper suggests that string theory in this background can be viewed as a maxed-out higher spin theory with a rich matter content organized by HSS representations, potentially guiding a unique, symmetry-determined string field theory on $AdS_3$.

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.