K\"ahlerian Effective Potentials for Chern-Simons-Matter Theories

TL;DR

This paper computes the K"ahlerian effective potential for Chern-Simons-matter theories describing multiple M2-branes, using superspace formalism to analyze both Abelian and non-Abelian cases.

Contribution

It provides explicit calculations of the superpropagators and the one-loop effective potential for Chern-Simons-matter theories in superspace, extending to non-Abelian cases.

Findings

Explicit superpropagators derived for the theories.

One-loop effective potential calculated.

Results applicable to multiple M2-brane models.

Abstract

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 K\"ahlerian effective potential for a Chern-Simons-matter theory. This calculation will be performed in $\mathcal{N} = 1$ 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.