SDiff Gauge Theory and the M2 Condensate

TL;DR

This paper develops a formalism for gauge theories with infinite-dimensional SDiff groups and applies it to describe M2-brane condensates using superconformal theories in three dimensions.

Contribution

It introduces a new formalism for constructing SDiff gauge theories and derives the ${ m N}=8$ superfield equations for the D=3 SDiff$_3$ superconformal theory.

Findings

Derived superfield equations for the SDiff$_3$ superconformal theory.

Established the relationship between M2-brane and D2-brane condensate theories.

Presented a pure-spinor superspace action for the SDiff$_3$ theory.

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 SDiff$_n$ of volume-preserving diffeomorphisms of some closed $n$-dimensional manifold. We then focus on the D=3 SDiff$_3$ superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its ${\cal N}=8$ 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.