The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

TL;DR

This paper analyzes the confined phase of (1+1)-dimensional massive Yang-Mills theory, deriving the spectrum of bound states analytically and discussing the implications of renormalization and lattice simulation results.

Contribution

It provides an analytical calculation of the meson-like spectrum in massive Yang-Mills theory using the exact sigma model S-matrix, highlighting the confined phase nature.

Findings

Spectrum of meson-like bound states derived analytically.

Evidence for confinement rather than Higgs phase in the continuum.

Lattice simulations support the confined phase at large volumes.

Abstract

Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic freedom of the sigma model. However, renormalization forces the gluon mass to infinity. The continuum theory is in a confined phase rather than a Higgs phase. The physical excitations of the system are hadron-like bound states of sigma model particles. We calculate the massive spectrum of meson-like bound states analytically, using the exact S-matrix of the sigma model. The baryon-like spectrum can be found in principle by solving a quantum mechanical N-body problem. We remark on the evidence for the confined phase found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their simulations show evidence for a Higgs-like phase which seems to disappear with increasing volume, finding agreement with our analysis in the continuum.