Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

TL;DR

This paper investigates how a self-dual background field influences confinement in SU(2) Yang-Mills theory, revealing a quadratic confining potential and exploring deconfinement at finite temperature.

Contribution

It demonstrates the emergence of a confining potential in a self-dual background and discusses the challenges of nonperturbative lattice calculations of the effective potential.

Findings

A quadratic confining potential arises in the presence of a self-dual background.

Deconfinement at finite temperature is analyzed via the effective potential.

Propagators in such backgrounds are entire functions, affecting confinement properties.

Abstract

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.