Higher-order string effective actions and off-shell d=4 supergravity

TL;DR

This paper reviews four-dimensional superspace supergravity, explores off-shell formulations for N=1,2, and studies supersymmetric R^4 corrections relevant to string theory black hole physics.

Contribution

It provides a comprehensive revision of superspace supergravity, details off-shell formulations for N=1,2, and constructs supersymmetric R^4 terms as string corrections.

Findings

Derived superspace actions for N=1,2 supergravities.

Presented solutions to Bianchi identities and field content.

Analyzed supersymmetrization of R^4 string correction terms.

Abstract

We start by a concise yet thorough revision of four-dimensional superspace supergravity. We present curved superspace geometry, for arbitrary N, including torsion, curvature and Bianchi identities. We motivate the choice of torsion constraints. We then consider the particular cases of N=1,2. In both cases we show how Poincare supergravity can be obtained from conformal supergravity. We see how to obtain the different versions of the Poincare off-shell theory, with distinct compensating multiplets and sets of auxiliary fields. For those versions of N=1,2 supergravities known as "old minimal", we present the solutions to the Bianchi identities, their field content and we show how to write superspace actions for these theories and their extensions using chiral densities and chiral projectors. As concrete applications, we study the supersymmetrization of the two possible R^4 terms in d=4, which are both required as string corrections to supergravity. We conclude by discussing possible applications of these results to open problems on black holes in string theory.