Dual Theory for maximally $\mathcal{N}$ extended flat Supergravity

TL;DR

This paper explores the duality between maximally extended 2+1 dimensional flat supergravity theories and a 1+1 dimensional chiral WZW model, revealing rich asymptotic structures and topological solutions.

Contribution

It introduces a dual quantum field theory description for maximally extended flat supergravity, connecting asymptotic symmetries to a chiral WZW model and flat super Liouville theory.

Findings

Identification of the dual chiral WZW model for the supergravity solutions

Connection of the phase space to flat super Liouville theory

Analysis of asymptotic symmetry algebra as a flat limit of superconformal algebra

Abstract

Maximally $\mathcal{N}$ extended $2+1$ dimensional flat Supergravity theories exist for a class of super-Poincar\'{e} algebras for arbitrary $\mathcal{N}$. They have rich asymptotic structures and contain all interesting topological supergravity solutions in presence of non-trivial holonomy. For the asymptotic symmetry algebra being a suitable flat limit of the superconformal algebra $Osp(\mathcal{N}|2;R)$, we have found the $1+1$ dimensional chiral WZW model as the dual quantum field theory that describes the dynamics of these solutions. In the Hamiltonian analysis, the reduced phase space resembles a flat super Liouville theory.