Instanton Calculations for N=1/ 2 super Yang-Mills Theory

TL;DR

This paper investigates instanton solutions in non-anticommutative N=1/2 super Yang-Mills theory, revealing modifications to anti-instantons and showing that the one-loop partition function remains unchanged from the standard theory.

Contribution

It provides explicit instanton solutions in non-anticommutative superspace and analyzes their effects on topological charge and quantum corrections, demonstrating the invariance of the one-loop partition function.

Findings

Anti-instantons receive quadratic fermionic and linear deformation corrections.

Topological charge density gains a quadratic C and quartic fermionic contribution.

The one-loop partition function remains identical to that of standard N=1 super Yang-Mills.

Abstract

We study (anti-) instantons in super Yang-Mills theories defined on a non anticommutative superspace. The instanton solution that we consider is the same as in ordinary SU(2) N=1 super Yang-Mills, but the anti-instanton receives corrections to the U(1) part of the connection which depend quadratically on fermionic coordinates, and linearly on the deformation parameter C. By substituting the exact solution into the classical Lagrangian the topological charge density receives a new contribution which is quadratic in C and quartic in the fermionic zero-modes. The topological charge turns out to be zero. We perform an expansion around the exact classical solution in presence of a fermionic background and calculate the full superdeterminant contributing to the one-loop partition function. We find that the one-loop partition function is not modified with respect to the usual N=1 super Yang-Mills.