Tachyon Condensation of D2/D4-Brane System in Noncommutative Gauge Theory

In this paper we construct the 2+1 effective theory of the light states in D2/D4-brane system in the context of noncommutative Yang-Mills theory. This effective theory is noncommutative and tachyonic, however, it is not taking the form of an Abelian Higgs model as naively expected. We solve the classical solutions of the effective theory which are nicely corresponding to different states during the tachyon condensation process of the dissolution of D2-brane into D4-brane. We also find that if the expected stable self-dual D0/D4 configuration as the unit-winding vortex exists, it would be highly calibrated in the effective theory and be out of the reach of the analytic solutions.