Adjoint fermion zero-modes for SU(N) calorons

TL;DR

This paper derives explicit formulas for adjoint fermion zero-modes in SU(N) caloron backgrounds, including periodic and antiperiodic cases, relevant for finite temperature supersymmetric Yang-Mills theory.

Contribution

It provides the first analytic expressions for adjoint zero-modes in SU(N) calorons with various boundary conditions, advancing semiclassical analyses at finite temperature.

Findings

Explicit formulas for zero-modes in different boundary conditions.

Application to finite temperature supersymmetric Yang-Mills theory.

Enhanced understanding of adjoint zero-modes in caloron backgrounds.

Abstract

We derive analytic formulas for the zero-modes of the Dirac equation in the adjoint representation in the background field of Q=1 SU(N) calorons. Solutions with various boundary conditions are obtained, including the physically most relevant cases of periodic and antiperiodic ones. The latter are essential ingredients in a semiclassical treatment of finite temperature supersymmetric Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other contexts is also presented.