Higgsing the stringy higher spin symmetry

TL;DR

This work probes the tensionless AdS$_3$ string/CFT duality by perturbing the symmetric orbifold of $\mathbb{T}^4$ with exactly marginal operators. Using conformal perturbation theory, it shows untwisted-sector moduli preserve the ${\\cal W}_{\\infty}[0]$ symmetry while twisted-sector moduli generate mass gaps, breaking the higher-spin symmetry down to ${\\cal N}=4$. Second-order calculations yield anomalous dimensions that arrange into Regge-like trajectories; the leading (quadratic) trajectory remains the lightest at fixed spin, and the anomalous dimensions grow as $\\gamma(s) \\\sim a \\\log s$ for large $s$, consistent with AdS$_3$ backgrounds with pure RR flux. The results support the picture that the symmetric orbifold corresponds to string theory in AdS$_3$ with RR flux and illuminate the organization of stringy higher-spin generators into Regge trajectories.

Abstract

It has recently been argued that the symmetric orbifold theory of T4 is dual to string theory on AdS3 x S3 x T4 at the tensionless point. At this point in moduli space, the theory possesses a very large symmetry algebra that includes, in particular, a $W_\infty$ algebra capturing the gauge fields of a dual higher spin theory. Using conformal perturbation theory, we study the behaviour of the symmetry generators of the symmetric orbifold theory under the deformation that corresponds to switching on the string tension. We show that the generators fall nicely into Regge trajectories, with the higher spin fields corresponding to the leading Regge trajectory. We also estimate the form of the Regge trajectories for large spin, and find evidence for the familiar logarithmic behaviour, thereby suggesting that the symmetric orbifold theory is dual to an AdS background with pure RR flux.