Fermionic determinant for SU(N) caloron with nontrivial holonomy

TL;DR

This paper analytically calculates the fermionic determinant in SU(N) caloron backgrounds with nontrivial holonomy, revealing insights into the quantum effects of monopole constituents at finite temperature.

Contribution

It provides the first analytical computation of the fermionic determinant for SU(N) calorons with nontrivial holonomy, focusing on the large separation limit between dyons.

Findings

Analytical expressions for the leading terms of the fermionic determinant.

Insights into the quantum structure of calorons with nontrivial holonomy.

Enhanced understanding of monopole contributions in finite-temperature gauge theories.

Abstract

In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of the SU(N) in the background of an instanton with non-trivial values of the Polyakov line at spatial infinity. This object, called the Kraan--van Baal -- Lee--Lu caloron, can be viewed as composed of N Bogomolny--Prasad--Sommerfeld monopoles (or dyons). We compute analytically two leading terms of the fermionic determinant at large separations between dyons.