  Based on recent developments, in this letter 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 a 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
obtain the D-branes world volume theory in the presence of background fluxes.
