U-Duality Symmetries from the Membrane Worldvolume

TL;DR

This paper investigates U-duality symmetries in M theory through the membrane worldvolume approach, identifying specific duality groups and their actions on background fields, especially in eight dimensions.

Contribution

It derives the U-duality groups for toroidally compactified M theory from the membrane perspective, including the explicit case of D=8 and its symmetry transformations.

Findings

Identifies U-duality groups for D>6 from membrane theory.

Derives the SL(2)xSL(3) U-duality group in D=8.

Verifies transformation properties by comparison with supergravity.

Abstract

We study U-duality symmetries of toroidally compactified M theory from the membrane worldvolume point of view. This is done taking the most general set of bosonic background fields into account. Upon restriction to pure moduli backgrounds, we are able to find the correct U-duality groups and moduli coset parameterizations for dimensions D>6 as symmetries of the membrane worldvolume theory. In particular, we derive the D=8 U-duality group SL(2)xSL(3). For general background fields, we concentrate on the case D=8. Though the SL(2) part of the symmetry appears to be obstructed by certain terms in the equations of motion, we are able to read off the transformation properties for the background fields. These transformations are verified by comparison with 11-dimensional supergravity dimensionally reduced to D=8.