$\mathcal{N} = (0, 2)$ higher-spin supergravity in AdS$_3$

TL;DR

This paper extends 3D higher-spin supergravity to include $ abla = (0, 2)$ supersymmetry, analyzing its asymptotic symmetry, matter content, and computing the 1-loop partition function in a thermal AdS background.

Contribution

It introduces the $ abla = (0, 2)$ supersymmetric extension of Vasiliev's higher-spin gravity in 3D and explores its asymptotic symmetry and quantum properties.

Findings

Asymptotic symmetry matches 2D $ abla = (0, 2)$ superconformal algebra.

Calculated 1-loop partition function for various matter fields.

Discussed potential matter content and linearized theory structure.

Abstract

In this paper we generalize Vasiliev's higher-spin gravity theory in 3d into $\mathcal{N} = (0, 2)$ case, by which we mean that the asymptotic symmetry of such a gravity theory have the structure of 2d $\mathcal{N} = (0, 2)$ superconformal algebra. While the construction is limited to linearized level, asymptotic symmetry and possible matter content of such theories is discussed. Also, the 1-loop partition function of this theory around thermal Euclidean AdS space-time, with different matter fields, is calculated by heat-kernel method.