Effective action of three-dimensional extended supersymmetric matter on gauge superfield background

TL;DR

This paper derives the low-energy effective actions for gauge superfields influenced by quantum N=2 and N=4 supersymmetric matter in three-dimensional space, using symmetry principles and quantum computations.

Contribution

It presents a general form of the N=2 gauge invariant and superconformal effective action, including higher order terms, and extends the results to N=4 gauge multiplets.

Findings

Derived the general form of the N=2 effective action fixed by symmetry.

Computed the arbitrary functions and coefficients via quantum calculations.

Extended the N=2 effective action to N=4 supersymmetric gauge multiplets.

Abstract

We study the low-energy effective actions for gauge superfields induced by quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski space. Analyzing the superconformal invariants in the N=2 superspace we propose a general form of the N=2 gauge invariant and superconformal effective action. The leading terms in this action are fixed by the symmetry up to the coefficients while the higher order terms with respect to the Maxwell field strength are found up to one arbitrary function of quasi-primary N=2 superfields constructed from the superfield strength and its covariant spinor derivatives. Then we find this function and the coefficients by direct quantum computations in the N=2 superspace. The effective action of N=4 gauge multiplet is obtained by generalizing the N=2 effective action.