  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.

High Energy Physics - Theory