One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions

Recent studies of the $AdS_4/CFT_3$ correspondence involve the construction of a peculiar supersymmetric gauge theory on the worldvolume of multiple M2s branes as a boundary field theory. Under suitable conditions the quantum theory becomes a noncommutative supersymmetric YM-CS gauge theory which call for an study of its renormalized perturbative corrections. As a preliminary step to more general consideration, the modification of the ${\cal N}=3,2,1$ supersymmetric YM-CS gauge theory due to noncommutativity of spatial coordinates is proposed. We carry out the one-loop renormalization and a noncommutative correction for the Chern-Simons coefficient is obtained. Finally it is found that this new correction depends of the noncommutative parameter in an analytic form.