Perturbing the symmetric orbifold from the worldsheet

TL;DR

This paper investigates how deforming the symmetric orbifold of T^4 affects its dual tensionless string theory in AdS3, matching anomalous dimensions through worldsheet perturbations.

Contribution

It identifies the worldsheet perturbation corresponding to the marginal deformation of the symmetric orbifold, confirming the duality's consistency.

Findings

Anomalous conformal dimensions are correctly reproduced from the worldsheet perspective.

The exactly marginal operator in the symmetric orbifold is matched with a specific worldsheet perturbation.

The study advances understanding of AdS/CFT duality away from the free point.

Abstract

The symmetric orbifold of $\mathbb{T}^4$ is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the $2$-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective.