U-duality covariant membranes

TL;DR

This paper develops a U-duality covariant formulation of membrane dynamics in eight dimensions, connecting supergravity fields, membrane charges, and automorphic forms, with solutions in specific backgrounds and discussions on supersymmetry.

Contribution

It introduces a fully U-duality covariant membrane action in D=8, linking membrane charges to automorphic representations and exploring their implications in supergravity.

Findings

Membrane charges are related to electric fluxes of world-volume 2-forms.

The formulation encodes interactions with eight-dimensional supergravity fields.

Solutions are provided for specific supergravity backgrounds.

Abstract

We outline a formulation of membrane dynamics in D=8 which is fully covariant under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to fields in the eight-dimensional supergravity, which is constructed through Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric fluxes determine the membrane charges, and are conjectured to provide an interpretation of the variables occurring in the minimal representation of E_{6(6)} which appears in the context of automorphic membranes. We solve the relevant equations for the action for a restricted class of supergravity backgrounds. Some comments are made on supersymmetry and lower dimensions.