Dual Description of Supergravity MacDowell-Mansouri Theory

TL;DR

This paper explores duality in MacDowell-Mansouri supergravity, demonstrating a dual theory with inverted couplings that forms a supersymmetric non-linear sigma model, highlighting challenges and insights in gravitational dualities.

Contribution

It introduces a dual formulation of supergravity with inverted couplings, connecting it to a supersymmetric non-linear sigma model of Freedman-Townsend type.

Findings

A dual theory with inverted couplings is constructed.

The dual theory is a supersymmetric non-linear sigma model.

Technical and conceptual challenges in finding effective duality are discussed.

Abstract

In the context of field theory two elements seem to be necessary to search for strong-weak coupling duality. First, a gauge theory formulation and second, supersymmetry. For gravitation these two elements are present in MacDowell-Mansouri supergravity. The search for an "effective duality" in this theory presents technical and conceptual problems that we discuss. Nevertheless, by means of a field theoretical approach, which in the abelian case coincides with $S$-duality, we exhibit a dual theory, with inverted couplings. This results in a supersymmetric non-linear sigma model of the Freedman-Townsend type.