Higher Spins & Strings

TL;DR

This paper demonstrates that the tensionless limit of string theory on AdS3 x S3 x T4 contains a Vasiliev higher spin subsector, explicitly connecting symmetric product orbifolds with higher spin algebras and symmetries.

Contribution

It explicitly shows the large level limit of N=4 cosets describes a higher spin subsector of the symmetric orbifold and reorganizes the partition function in terms of $W_{}$ representations.

Findings

Large level limit of N=4 cosets describes a higher spin subsector.

Partition function reorganized in terms of $W_{}$ algebra representations.

Unbroken stringy symmetries form an extended $W_{}$-based chiral algebra.

Abstract

It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $W_{\infty}$ representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.