A dual formulation of supergravity-matter theories

TL;DR

This paper introduces a dual formulation of N=1 supergravity-matter theories that simplifies constructing supersymmetric AdS solutions, extending beyond the limitations of old minimal supergravity.

Contribution

It develops a dual formulation for supergravity-matter systems that overcomes previous restrictions, incorporating matter and cosmological constants.

Findings

Constructed a dual formulation for supergravity-matter theories.

Unified the sigma-model action into a single supervolume term.

Proposed a general form for supercurrents in AdS.

Abstract

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N=1 supergravity-matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal (n=-1) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kahler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.