# Even spin $\mathcal{N}=4$ holography

## TL;DR

This paper constructs a 2D vector model with small  superconformal symmetry, explores its algebraic structure, and proposes its duality to a higher spin theory in AdS3, connecting to tensionless string backgrounds.

## Contribution

It introduces a new  superconformal vector model and establishes its holographic duality to a minimal Vasiliev higher spin theory in AdS3.

## Key findings

- The vector model's chiral algebra is generated by superprimary fields of even conformal weight.
- The model is the large level limit of a coset theory with large  symmetry.
- The relation to symmetric product orbifolds and tensionless strings in AdS3  S3  T4 is elucidated.

## Abstract

A two-dimensional Sp($2N$) vector model with small $\mathcal{N}=4$ superconformal symmetry is formulated, and its chiral algebra is shown to be generated by superprimary fields of even conformal weight. This vector model is the large level limit of a coset theory with large $\mathcal{N}=4$, whose proposed AdS$_3$ dual is a minimal Vasiliev higher spin theory with gauge algebra generated by fields of even spin. The relation of this vector model to the symmetric product orbifold, dual to tensionless strings in AdS$_3$ $\times$ S$^3$ $\times$ $\mathbb{T}^4$, is also worked out.