Noncommutative Monopole at the Second Order in \theta

TL;DR

This paper investigates noncommutative monopole solutions at second order in , demonstrating how to match scalar eigenvalues with D-brane configurations by tuning parameters in the Seiberg-Witten map.

Contribution

It provides a detailed second-order analysis of noncommutative monopoles and shows how physical conditions fix ambiguities in the Seiberg-Witten map.

Findings

Scalar eigenvalues match tilted D-string configurations

Higher order SW map ambiguities can be fixed by physical requirements

Explicit second-order solutions in noncommutative super Yang-Mills theory

Abstract

We study the noncommutative U(2) monopole solution at the second order in the noncommutativity parameter \theta^{ij}. We solve the BPS equation in noncommutative super Yang-Mills theory to O(\theta^2), transform the solution to the commutative description by the Seiberg-Witten (SW) map, and evaluate the eigenvalues of the scalar field. We find that, by tuning the free parameters in the SW map, we can make the scalar eigenvalues precisely reproduce the configuration of a tilted D-string suspended between two parallel D3-branes. This gives an example of how the ambiguities inevitable in the higher order SW map are fixed by physical requirements.