Mass deformation of the multiple M2-branes theory

Based on recent developments, in this paper we study the one parameter deformation of 2 + 1-dimensional gauge theories with scale invariance and N = 8 supersymmetry, which is expected to be the field theory living on a stack of M2-branes. The deformed gauge theory is defined by the Lagrangian and is based on an infinite set of novel 3-algebras constructed by relaxing the assumption that the invariant metric is positive definite. Under the Higgs mechanism, we can develop the D-branes world volume theory in the presence of background fluxes.