Unstable solitons in noncommutative gauge theory

Abstract

We find a class of exact solutions of noncommutative gauge theories corresponding to unstable non-BPS solitons. In the two-dimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find localized solutions carrying nonzero magnetic flux. In four euclidean dimensions we find non-BPS solutions with the same Pontrjagin charge but greater energy than the usual self-dual Yang-Mills instanton. We conjecture that these solutions and generalizations thereof correspond to nonsupersymmetric configurations of D(p-2k)-branes (or intersections thereof) in a Dp-brane in the noncommutative scaling limit of large B-field. In the particular case of a 0-brane on a 2-brane the analysis of small fluctuations reveals an infinite tower of states which agrees exactly with that of the 0-2 CFT in the scaling limit. The spectrum contains a tachyon, and we show explicitly that the endpoint of tachyon condensation corresponds to the 0-brane dissolved in the 2-brane.