Properties of the SU(N_c) Yang-Mills vacuum state

TL;DR

This paper investigates the properties of the Yang-Mills vacuum state, analyzing its energy behavior at extreme parameters, vacuum degeneracy, and the role of monopole condensation, providing new insights into non-perturbative quantum field theory.

Contribution

It offers a new interpretation of the vacuum energy density behavior and discusses the vacuum degeneracy and monopole condensation in SU(N_c) Yang-Mills theory.

Findings

Vacuum energy density behaves asymptotically at large imaginary theta.

Vacuum is doubly degenerate at theta=pi.

Monopole field condensation potential is derived.

Abstract

The asymptotic behaviour of the vacuum energy density, ${\bar E}(\theta)$, at $\theta \ra \pm i \infty$ is found out. A new interpretation and a qualitative discussion of the ${\bar E}(\theta)$ behaviour are presented. It is emphasized that the vacuum is doubly degenerate at $\theta=\pi$, and the quark electric string can terminate on the domain wall interpolating between these two vacua. The potential of the monopole field condensing in the Yang-Mills vacuum is obtained.