Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction

Abstract

We study an extension of the ADHM construction to give deformed anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n) gauge group. First we extend the exterior algebra on superspace to non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory can be reformulated in a geometrical way. By using this exterior algebra, we formulate a non(anti)commutative version of the super ADHM construction and show that the curvature two-form superfields obtained by our construction do satisfy the deformed ASD equations and thus we establish the deformed super ADHM construction. We also show that the known deformed U(2) one instanton solution is obtained by this construction.