Three-forms, dualities and membranes in four-dimensional supergravity

TL;DR

This paper explores how double three-form multiplets in 4D supergravity models promote flux parameters to dynamical variables, revealing their transformation under dualities and coupling to membranes, with applications to BPS domain walls.

Contribution

It demonstrates the natural transformation of double three-form multiplets under symplectic dualities and develops a duality covariant, supersymmetric framework for membrane couplings in supergravity.

Findings

Double three-form multiplets transform under symplectic dualities.

Membrane couplings are supersymmetric, kappa-symmetric, and duality covariant.

Derived flow equations for BPS domain walls sourced by membranes.

Abstract

We consider four-dimensional $\mathcal{N}=1$ supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can promote to dynamical variables (part of) the quantized numbers appearing in the flux-induced superpotential. We show that double three-form multiplets naturally transform under symplectic dualities associated with the special K\"ahler structure that characterizes their scalar sector. Furthermore, we discuss how to couple membranes which carry arbitrary `electric-magnetic' charges. The complete action is supersymmetric, kappa-symmetric and duality covariant. As an application, we derive the flow equations for BPS domain walls sourced by membranes and give simple analytic examples of their solution.