# On tensionless string field theory in AdS$_3$

## TL;DR

This paper advances the formulation of tensionless string field theory in AdS3 by proposing gauge-invariant equations that encompass the full spectrum, including twisted sectors, and relate to higher spin symmetries.

## Contribution

It introduces a set of gauge-invariant field equations for tensionless strings in AdS3, incorporating the full spectrum and interactions, based on the higher spin algebra 'Higher Spin Square.'

## Key findings

- The equations include the full perturbative spectrum, including twisted sectors.
- Linearization yields decoupled wave equations consistent with expectations.
- The framework can be extended to other large-N symmetric orbifolds.

## Abstract

We report on progress in formulating a field theory of tensionless strings in $AdS_3$, starting from the dual large-$N$ symmetric orbifold CFT. We propose a set of field equations which are gauge invariant under the higher spin algebra of the theory, the `Higher Spin Square'. The massless higher spin sector is captured by a Chern-Simons gauge field, while the matter sector is described by unfolded equations similar to those appearing in Vasiliev theory. Our equations incorporate the full perturbative spectrum of the theory, including states coming from the twisted sectors, and capture some of the interactions fixed by gauge invariance. We also discuss the spectrum of the bulk theory and explain how linearization around $AdS_3$ gives rise to the expected set of decoupled wave equations. Our results can be generalized to describe bulk duals of other large-$N$ symmetric orbifolds.