Multiple M2-Branes and Plane Waves

TL;DR

This paper extends the BLG model for multiple M2-branes to curved plane wave backgrounds, verifying its consistency through reductions and algebraic properties, and relates different coordinate formulations of the theory.

Contribution

It introduces a generalized M2-brane action in curved backgrounds and demonstrates its equivalence to known theories via reductions and algebraic consistency checks.

Findings

The generalized action correctly captures plane wave geometries.

M2 to D2 reduction yields the D2-brane Yang-Mills theory with a null-dependent dilaton.

Rosen and Brinkmann coordinate formulations are shown to be equivalent.

Abstract

We propose a natural generalisation of the BLG multiple M2-brane action to membranes in curved plane wave backgrounds, and verify in two different ways that the action correctly captures the non-trivial space-time geometry. We show that the M2 to D2 reduction of the theory along a non-trivial direction in field space is equivalent to the D2-brane world-volume Yang-Mills theory with a non-trivial (null-time dependent) dilaton in the corresponding IIA background geometry. As another consistency check of this proposal we show that the properties of metric 3-algebras ensure the equivalence of the Rosen coordinate version of this action (time-dependent metric on the space of 3-algebra valued scalar fields, no mass terms) and its Brinkmann counterpart (constant couplings but time-dependent mass terms). We also establish an analogous result for deformed Yang-Mills theories in any dimension which, in particular, demonstrates the equivalence of the Rosen and Brinkmann forms of the plane wave matrix string action.