# Chiral Higher Spin Gravity

## TL;DR

This paper constructs a comprehensive chiral higher spin gravity theory in AdS$_3$, revealing its boundary conditions, asymptotic symmetries, and dependence on multiple functions, advancing the understanding of higher spin holography.

## Contribution

It introduces the most general chiral higher spin theory with specific boundary conditions and detailed symmetry algebra, extending previous models with a broader set of functions.

## Key findings

- The metric matches the most general AdS$_3$ boundary conditions.
- Asymptotic symmetry algebra is a product of $ ext{W}_3$ and affine $sl(3)_k$.
- The theory depends on 19 functions, generalizing prior work.

## Abstract

We construct a candidate for the most general chiral higher spin theory with AdS$_3$ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are $19$ functions. Despite this, we show that the resulting metric has the form of the "most general" AdS$_3$ boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a $\mathcal{W}_3$ algebra on the left and an affine $sl(3)_k$ current algebra on the right, as desired. The metric and higher spin fields depend on all the $19$ functions. We compare our work with previous results in the literature.