Brane Configuration from Monopole Solution in Non-Commutative Super Yang-Mills Theory

TL;DR

This paper investigates monopole configurations in non-commutative super Yang-Mills theory, revealing non-local structures consistent with brane-configuration predictions, through solving BPS and eigenvalue equations to first order in non-commutativity.

Contribution

It provides a detailed analysis of monopole solutions in non-commutative super Yang-Mills theory and connects these solutions to brane configurations, confirming theoretical predictions.

Findings

Monopoles exhibit non-locality in non-commutative space.

Solutions match predictions from brane-configuration techniques.

First-order non-commutativity effects are explicitly calculated.

Abstract

We study the structure of the monopole configuration in U(2) non-commutative super Yang-Mills theory. Our analysis consists of two steps: solving the BPS equation and then the eigenvalue equation in the non-commutative space. Calculation to the first non-trivial order in the non-commutativity parameter theta shows that the monopole exhibits a certain non-locality. This structure is precisely the one expected from the recent predictions by the brane-configuration technique.