The Small ${\cal N}=4$ Superconformal ${\cal W}_{\infty}$ Algebra

TL;DR

This paper investigates the symmetry algebra of the symmetric orbifold of T^4, providing evidence that it is a highly symmetrical conformal field theory with no deformation parameters, relevant for string theory on AdS3 backgrounds.

Contribution

It identifies the structure of the small N=4 superconformal W_infinity algebra in the symmetric orbifold of T^4 and shows it lacks deformation parameters, indicating maximal symmetry.

Findings

Symmetric orbifold of T^4 has a highly symmetrical algebra.

The algebra likely has no deformation parameters.

Supports the idea of the orbifold being a maximally symmetric CFT.

Abstract

The symmetric orbifold of $\mathbb{T}^4$ is the CFT dual of string theory on AdS$_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation parameter. This suggests that the symmetric orbifold is (at least locally) the most symmetrical CFT in its moduli space.