Seiberg-Witten transforms of noncommutative solitons

Abstract

We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the Seiberg-Witten transform of the U(2) instanton and show that it has a finite size determined by the noncommutative scale and by the deformation parameter ρ. For large ρ, the profile of the D0-brane density of the instanton agrees surprisingly well with that of the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton on commutative space.