SDiff gauge theory and the M2 condensate

Abstract

We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff 2 super-Yang-Mills theory describing a condensate of D2-branes. © 2009 SISSA.