Maximal supergravity in three dimensions: supergeometry and differential forms

TL;DR

This paper develops a detailed superspace formulation of three-dimensional maximal supergravity, explicitly constructing supergeometric structures and p-form field strengths, and discusses gauged extensions within this framework.

Contribution

It provides a comprehensive supergeometric and differential forms analysis of 3D maximal supergravity, including explicit constructions and gauged theory considerations.

Findings

Explicit supergeometry for 3D maximal supergravity

Construction of p-form field strengths using supersymmetry and E8

Discussion of gauged supergravity extensions

Abstract

The maximal supergravity theory in three dimensions, which has local SO(16) and rigid $E_8$ symmetries, is discussed in a superspace setting starting from an off-shell superconformal structure. The on-shell theory is obtained by imposing further constraints. It is essentially a non-linear sigma model that induces a Poincar\'e supergeometry that is described in detail. The possible $p$-form field strengths, for $p=2,3,4$, are explicitly constructed using supersymmetry and $E_8$. The gauged theory is also discussed.