BPS-type equations in the non-anticommutative N=2 supersymmetric U(1) gauge theory

TL;DR

This paper explores BPS-like equations in a non-anticommutative N=2 supersymmetric U(1) gauge theory, establishing their solvability, consistency with equations of motion, and restrictions on scalar fields, with brief discussion on supersymmetry.

Contribution

It introduces and proves the solvability of new BPS-like equations in non-anticommutative N=2 supersymmetric gauge theory, extending abelian (anti)self-duality conditions.

Findings

BPS-like equations are fully solvable and consistent with equations of motion.

Restrictions on scalar field values are identified.

Brief discussion on the residual supersymmetry is provided.

Abstract

We investigate the equations of motion in the four-dimensional non-anticommutative N=2 supersymmetric U(1) gauge field theory, in the search for BPS configurations. The BPS-like equations, generalizing the abelian (anti)self-duality conditions, are proposed. We prove full solvability of our BPS-like equations, as well their consistency with the equations of motion. Certain restrictions on the allowed scalar field values are also found. Surviving supersymmetry is briefly discussed too.