# Equivalent Dual Theories for 3D N=2 Supergravity

## TL;DR

This paper demonstrates that 3D N=2 supergravity with R-symmetry can be equivalently described by a flat limit of a generalized Liouville theory or a gauged chiral WZW model, sharing the same symmetries.

## Contribution

It establishes an equivalence between two different reduced phase space descriptions of 3D N=2 supergravity, revealing their common gauge and quantum super-BMS$_3$ symmetries.

## Key findings

- Both descriptions have identical gauge symmetries.
- Both descriptions share the same quantum super-BMS$_3$ symmetry.
- The reduced phase space is a flat limit of a generalized Liouville theory.

## Abstract

N=2 three dimensional Supergravity with internal $R-$symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be flat limit of a generalised Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum N=2 superBMS$_3$) symmetries.