Gluino zero-modes for non-trivial holonomy calorons

TL;DR

This paper calculates gluino zero-modes in the background of SU(2) calorons with non-trivial holonomy, providing insights relevant for semiclassical analysis of N=1 Super-symmetric Yang-Mills theory.

Contribution

It presents explicit formulas for gluino zero-modes in caloron backgrounds with non-trivial holonomy, advancing understanding of fermionic solutions in supersymmetric gauge theories.

Findings

Zero-modes can be constructed from linear combinations of two contributions.

Formulas relate zero-modes to caloron field strength and vector potential.

Results are relevant for semiclassical studies of supersymmetric Yang-Mills.

Abstract

We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.