Noncommutative/Nonlinear BPS Equations without Zero Slope Limit

TL;DR

This paper demonstrates that the relation between noncommutative and commutative BPS equations persists without the zero slope limit, providing evidence for their connection and solving the non-linear instanton equation exactly.

Contribution

It shows the noncommutative and commutative BPS equations are related beyond the zero slope limit, extending the understanding of their connection in non-Abelian Born-Infeld theory.

Findings

Relation holds without zero slope limit.

Exact solution of the non-linear instanton equation.

Supports the conjecture of BPS equation correspondence.

Abstract

It is widely believed that via the Seiberg-Witten map, the linearly realized BPS equation in the non-commutative space is related to the non-linearly realized BPS equation in the commutative space in the zero slope limit. We show that the relation also holds without taking the zero slope limit as is expected from the arguments of the BPS equation for the non-Abelian Born-Infeld theory. This is regarded as an evidence for the relation between the two BPS equations. As a byproduct of our analysis, the non-linear instanton equation is solved exactly.