Solitons in Noncommutative Gauge Theory

TL;DR

This paper provides a comprehensive analysis of classical solutions in noncommutative gauge theories, including stable BPS states and monopoles, with implications for D-brane configurations in string theory.

Contribution

It offers a unified framework for solutions in noncommutative gauge theories, including explicit classifications and new analytic monopole solutions, connecting gauge theory to string theory brane setups.

Findings

Classified all solutions of 2D noncommutative Yang-Mills equations.

Identified stable BPS solutions corresponding to D1-D3 brane systems.

Constructed an exact analytic U(2) monopole solution.

Abstract

We present a unified treatment of classical solutions of noncommutative gauge theories. We find all solutions of the noncommutative Yang-Mills equations in 2 dimensions; and show that they are labelled by two integers -- the rank of gauge group and the magnetic charge. The magnetic vortex solutions are unstable in 2+1 dimensions, but correspond to the full, stable BPS solutions of N=4 U(1) noncommutative gauge theory in 4 dimensions, that describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B field in the Seiberg-Witten limit. We discuss the behaviour of gauge invariant observables in the background of the solitons. We use these solutions to construct a panoply of BPS and non-BPS solutions of supersymmetric gauge theories that describe various configurations of D-branes. We analyze the instabilities of the non-BPS solutions. We also present an exact analytic solution of noncommutative gauge theory that describes a U(2) monopole.