Superfield formalism for the one loop effective action and CP(N) model in three dimensions

TL;DR

This paper develops a systematic method to compute the supertrace in superspace, enabling the calculation of one-loop effective actions while preserving supersymmetry, and applies it to a three-dimensional N=1 supersymmetric CP(N) model.

Contribution

It introduces a general formula for the supertrace in superspace, facilitating explicit one-loop effective action calculations in superfield theories.

Findings

Derived a formula expressing supertrace as a superspace integral

Applied the method to a 3D N=1 supersymmetric CP(N) model

Found the one-loop effective action corresponds to supersymmetric Maxwell-Chern-Simons theory

Abstract

To obtain the one loop effective action for a given superfield theory, one encounters the notion such as the `supertrace' of a differential operator on superspace. We develop, in a systematic way for the superspace of arbitrary dimension, a method to determine the supertrace precisely. We present a formula to express the supertrace explicitly as the superspace integral, which enables us to write the one loop effective action within the superfield formalism and still maintain the manifest supersymmetry. In the second part of the paper, we apply the result to a three dimensional N=1 supersymmetric CP(N) model in the auxiliary superfield formalism. The model contains a novel topological interaction term. We show in the large N limit the one loop effective action is given by the supersymmetric Maxwell-Chern-Simons theory.