Solitons in non-commutative gauge theory

Abstract

We present a unified treatment of classical solutions of non-commutative gauge theories. We find all solutions of the non-commutative Yang-Mills equations of motion in 2 dimensions; and show that they are labeled by two integers - the rank of the 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) non-commutative 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 α′ → 0 limit. We discuss the behavior 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 instabilites of the non-BPS solitons. We also present an exact analytic solution of non-commutative gauge theory that describes a U(2) monopole.