Deformed Nahm Equation and a Noncommutative BPS Monopole
Dongsu Bak
TL;DR
This paper derives a deformed Nahm equation for noncommutative supersymmetric Yang-Mills theory and constructs a monopole solution, revealing that noncommutativity introduces a U(1) magnetic dipole component.
Contribution
It introduces a deformed Nahm equation for noncommutative BPS monopoles and explicitly constructs a monopole solution to linear order in noncommutativity.
Findings
Leading order correction affects only the U(1) sector.
The U(1) magnetic field exhibits a long-range magnetic dipole moment.
The solution provides insight into noncommutative monopole structure.
Abstract
A deformed Nahm equation for the BPS equation in the noncommutative N=4 supersymmetric U(2) Yang-Mills theory is obtained. Using this, we constructed explicitly a monopole solution of the noncommutative BPS equation to the linear order of the noncommutativity scale. We found that the leading order correction to the ordinary SU(2) monopole lies solely in the overall U(1) sector and that the overall U(1) magnetic field has an expected long range component of magnetic dipole moment.
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