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

Abstract

A bstract We consider four-dimensional $$ \mathcal{N}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> 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 Kähler 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.