Aspects of supersymmetry in multiple membrane theories

Abstract

This thesis consists of two parts. In the rst part we investigate the worldvolume supersymmetry algebra of multiple membrane theories. We begin with a description of M-theory branes and their intersections from the perspective of spacetime and worldvolume supersymmetry algebras. We then provide an overview of the recent work on multiple M2-branes focusing on the Bagger-Lambert theory and its relation to the Nambu-Poisson M5-brane and the ABJM theory. The worldvolume supersymmetry algebras of these theories are explicitly calculated and the charges interpreted in terms of spacetime intersections of M-branes. The second part of the thesis looks at l3 p corrections to the supersymmetry transformations of the Bagger-Lambert theory. We begin with a review of the dNS duality transformation which allows a gauge eld to be dualised to a scalar eld in 2+1 dimensions. Applying this duality to 02 terms of the non-abelian D2-brane theory gives rise to the l3 p corrections of the Lorentzian Bagger-Lambert theory. We then apply this duality transformation to the 02 corrections of the D2-brane supersymmetry transformations. For the `abelian' Bagger-Lambert theory we are able to uniquely determine the l3 p corrections to the supersymmetry transformations of the scalar and fermion elds. Generalising to the `non-abelian' Bagger-Lambert theory we are able to determine the l3 p correction to the supersymmetry transformation of the fermion eld. Along the way make a number of observations relating to the implementation of the dNS duality transformation at the level of supersymmetry transformations.