Non-Linear/Non-Commutative Non-Abelian Monopoles

TL;DR

This paper derives non-linear BPS equations for U(2) monopoles and instantons in non-Abelian gauge theory with background B-field, showing their equivalence to non-commutative anti-self-dual equations through the Seiberg-Witten map.

Contribution

It introduces non-linear BPS equations in non-Abelian gauge theory with background B-field and demonstrates their equivalence to non-commutative equations via the Seiberg-Witten map.

Findings

Derived non-linear BPS equations for U(2) monopoles and instantons.

Established the equivalence with non-commutative anti-self-dual equations.

Connected non-linear supersymmetry corrections to non-commutative gauge theory.

Abstract

Using recently proposed non-linearly realized supersymmetry in non-Abelian gauge theory corrected to the order (alpha')^2, we derive the non-linear BPS equations in the background B-field for the U(2) monopoles and instantons. We show that these non-Abelian non-linear BPS equations coincide with the non-commutative anti-self-dual equations via the Seiberg-Witten map.