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

TL;DR

This paper extends the ADHM construction to generate deformed instantons in N=1/2 super Yang-Mills theory using a non(anti)commutative superspace framework, providing a geometric reformulation and explicit solutions.

Contribution

It introduces a non(anti)commutative super ADHM construction that produces deformed instanton solutions in N=1/2 super Yang-Mills theory, expanding the mathematical toolkit for such theories.

Findings

Deformed super ADHM construction satisfies deformed ASD equations.

Reformulation of N=1/2 super Yang-Mills in non(anti)commutative superspace.

Explicit deformed U(2) one-instanton solution obtained.

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.