Solitons in Noncommutative Gauge Theory

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.