SU(N) Gauge Theories with C-Periodic Boundary Conditions: II. Small Volume Dynamics

TL;DR

This paper studies the quantum stability and spectrum of SU(N) gauge theories with C-periodic boundary conditions in small volumes, identifying stable classical vacua and analyzing their quantum properties.

Contribution

It identifies stable toron solutions in SU(N) gauge theories with C-periodic boundary conditions and analyzes their quantum stability and spectral implications.

Findings

Stable torons break cubic symmetry.

Quartic modes exist at stable torons.

Effective Hamiltonian computed to one loop.

Abstract

The dynamics of SU(N) gauge theories, especially for N=3, in a small C-periodic box are investigated. We identify the fields that mimimize the energy---the torons---and determine which of these ``classical'' vacua are stable quantum mechanically. The stable torons break cubic symmetry, which has interesting consequences on the spectrum. At any of the stable torons there are also quartic modes. Since all C-periodic boundary conditions are gauge-equivalent, we choose a convenient version, for which the quartic modes are constant modes, and compute the effective Hamiltonian to one loop in perturbation theory.