(p,q) D=3 Poincare supergravities from Lie algebra expansions

TL;DR

This paper derives three-dimensional (p,q)-Poincare supergravity theories as Chern-Simons gauge theories using Lie algebra expansion methods, providing a systematic way to construct these models from superalgebra expansions.

Contribution

It introduces a novel application of Lie algebra expansion techniques to derive (p,q)-Poincare supergravities as Chern-Simons theories from simple superalgebras.

Findings

Derived (p,0)-Poincare supergravity as a CS theory from osp(p|2;R) expansion.

Constructed general (p,q)-Poincare superalgebras and their supergravity actions.

Provided a systematic algebraic framework for supergravity models in three dimensions.

Abstract

We use the expansion of superalgebras procedure (summarized in the text) to derive Chern-Simons (CS) actions for the (p,q)-Poincare supergravities in three-dimensional spacetime. After deriving the action for the (p,0)-Poincare supergravity as a CS theory for the expansion osp(p|2;R)(2,1) of osp(p|2;R), we find the general (p,q)-Poincare superalgebras and their associated D=3 supergravity actions as CS gauge theories from an expansion of the simple osp(p+q|2,R) superalgebras, namely osp(p+q|2,R)(2,1,2).