Two-loop superfield effective potential for a $\mathcal{N}=2$, $d=3$ supersymmetric quantum electrodynamics with higher derivatives

TL;DR

This paper computes the two-loop superfield effective potential for a higher-derivative $ ext{N}=2$, $d=3$ supersymmetric QED, providing a closed-form expression in the K"{a}hlerian approximation.

Contribution

It introduces a higher-derivative generalization of $ ext{N}=2$, $d=3$ supersymmetric QED and explicitly calculates its superfield effective potential up to two loops.

Findings

Effective potential obtained in closed form.

Superfield effective potential expressed in elementary functions.

Two-loop corrections explicitly calculated.

Abstract

In the $\mathcal{N}=2$, $d=3$ superspace, we consider a higher-derivative generalization of the supersymmetric quantum electrodynamics, where the higher-derivative operator is a polynomial function of the d'Alembertian with arbitrary degree. For this theory, we use the background field quantization in a higher-derivative $R_\xi$ gauge to explicitly calculate the superfield effective potential up to two loops in the K\"{a}llerian approximation. This superfield effective potential is obtained in a closed form and in terms of elementary functions.