Preliminary study of two-dimensional SU(N) Yang-Mills theory with adjoint matter by Hybrid Monte Carlo approach

TL;DR

This paper presents initial Monte Carlo simulation results for two-dimensional SU(N) Yang-Mills theories with adjoint matter, aiming to verify analytic predictions and explore confinement phenomena.

Contribution

It introduces a Hybrid Monte Carlo approach to study these models, providing the first numerical checks of prior analytic and light-cone quantization results.

Findings

Initial numerical results obtained for the models

Verification of some analytic predictions

Insights into charge confinement in 2D gauge theories

Abstract

Two-dimensional non-abelian quantum field models provide a useful laboratory for analytic and numerical investigations of quantum theories with gauge symmetry. They can exhibit various features, such as charge confinement, which are known from D=4 theories like QCD. Several analytic predictions concerning the spectra of two-dimensional systems with adjoint matter were postulated and numerical results were obtained using Discrete Light Cone Quantization techniques, however none of them has been checked via Monte Carlo simulations. In this Letter we present two such models which are particularly interesting from the physical point of view and discuss first numerical results.