Supergravity in (2+1) dimensions from (3+1)-dimensional Supergravity

TL;DR

This paper demonstrates how (2+1)-dimensional supergravity can be derived from (3+1)-dimensional supergravity using a gauge theory formalism, ensuring consistent gauge symmetry reduction.

Contribution

It provides a novel method to obtain lower-dimensional supergravity theories via dimensional reduction within a gauge theory framework.

Findings

Chern-Simons supergravity derived from higher dimensions

Consistent gauge symmetry mapping between dimensions

Framework applicable to other gauge theories

Abstract

In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3+1)-dimensional supergravity, when written as a gauge theory of the Poincare group. The dimensional reductions are consistent with the gauge symmetries, mapping (3+1)-dimensional Poincare supergroup gauge transformations onto (2+1)-dimensional Poincare supergroup ones.