Aspects of Multiple Membranes

TL;DR

The paper addresses the problem of obtaining a consistent worldvolume description of coincident membranes and their relation to fivebranes in M‑theory by analyzing the Bagger–Lambert theory with fields valued in a non‑associative 3‑algebra and a twisted Chern–Simons gauge sector. It shows that open membranes yield a six‑dimensional boundary theory consistent with a self‑dual string in the fivebrane, with a near‑horizon geometry described by $AdS_3\times S^3$, and connects this to holographic duality. The authors then construct and study marginal deformations of the membrane theory that preserve ${\cal N}=2$ supersymmetry, via a beta‑like deformation implemented through a star‑product on the triple product, and relate these to deformations of the corresponding supergravity dual. Two explicit examples illustrate how the deformation acts on associators and how some choices reproduce the expected dual perturbations, while others introduce new phase structures. Overall, the work advances toward a coherent interacting membrane framework, linking boundary fivebrane physics to bulk holography and providing a structured path to explore gravity duals through marginal deformations.

Abstract

This paper examines various aspects of the recently proposed theory of coincident membranes by Bagger and Lambert. These include the properties of open membranes and the resulting boundary theory with an interpretation in terms of the fivebrane and marginal supersymmetric deformations of the interactions with the relation to the holographic dual.