Higher Spins & Strings

TL;DR

The paper demonstrates that string theory at the tensionless point on ${ m AdS}_3 imes{ m S}^3 imes{ m T}^4$ contains a closed subsector described by a Vasiliev-like higher-spin theory, and that the full symmetric product orbifold can be reorganized into representations of an extended ${ m W}_{ abla}[0]$ algebra. This is done by connecting the large ${ m N}=4$ Wolf space cosets to a continuous ${ m U}(N)$ orbifold in the $k oty$ limit, and embedding this into the symmetric product orbifold via $S_{N+1} o { m U}(N)$, so that the untwisted sector matches the perturbative higher-spin content while the full spectrum forms a non-diagonal modular invariant of ${ m W}_{ abla}[0]$. The work also analyzes twisted sectors, showing how ground states, fermionic excitations, and BPS states map to coset primaries, and explains why light states do not lift to string theory when the extended symmetry is enforced. Overall, the results provide a concrete algebraic framework for understanding the relationship between higher-spin symmetries and stringy symmetries in the tensionless limit, with implications for Higgsing and the construction of duals to more general AdS$_3$ backgrounds.

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.