Kählerian effective potentials for Chern–Simons-matter theories

In this paper, we will calculate the effective potential for a theory of multiple M2-branes. As the theory of multiple M2-branes can be described by a Chern–Simons-matter theory, this will be done by calculating the Kählerian effective potential for a Chern–Simons-matter theory. This calculation will be performed in N=1N=1 superspace formalism. We will initially study an Abelian Chern–Simons-matter theory, and then generalize those results to the full non-Abelian Chern–Simons-matter theory. We will obtain explicit expressions for the superpropagators for this theory. These superpropagators will be used to calculate the one-loop effective potential.