Instantons and Matter in N=1/2 Supersymmetric Gauge Theory

TL;DR

This paper extends instanton calculus in N=1/2 supersymmetric gauge theory with a massless flavor, solving equations exactly in the non(anti)commutativity parameter and analyzing the effects on the effective action and gluino condensate.

Contribution

It introduces a detailed solution of instanton equations with matter in N=1/2 supersymmetry, including new terms in the effective action that preserve invariance.

Findings

The matter superfield profile is deformed by linear and quadratic C corrections.

The instanton effective action gains a C^2 contribution that remains N=1/2 invariant.

The gluino condensate is unaffected by the new effective action terms.

Abstract

We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity parameter C. The profile of the matter superfield is deformed through linear and quadratic corrections in C. Higher order corrections are absent because of the fermionic nature of the back-reaction. The instanton effective action, in addition to the usual 't Hooft term, includes a contribution of order C^2 and is N=1/2 invariant. We argue that the N=1 result for the gluino condensate is not modified by the presence of the new term in the effective action.