(2+1)-Dimensional Yang-Mills Theory and Form Factor Perturbation Theory

TL;DR

This paper investigates (2+1)-dimensional Yang-Mills theory by leveraging integrable (1+1)-dimensional sigma models, deriving new exact form factors, and calculating physical quantities like string tensions and glueball spectra, with a focus on anisotropic correlations.

Contribution

It introduces a novel approach to compute physical quantities in (2+1)D Yang-Mills theory using form factors from integrable sigma models, extending previous results to anisotropic cases.

Findings

Calculated string tensions and glueball spectra in (2+1)D Yang-Mills.

Derived new exact form factors and correlation functions.

Analyzed anisotropic correlation functions in different spatial directions.

Abstract

We study Yang Mills theory in 2+1 dimensions, as an array of coupled (1+1)-dimensional principal chiral sigma models. This can be understood as an anisotropic limit where one of the space-time dimensions is discrete and the others are continuous. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. New exact form factors and correlation functions of the sigma model have recently been found by the author and P. Orland. In this paper, we use these new results to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results by Orland, which include the string tensions and the low-lying glueball spectrum. We also present a new approach to calculate two-point correlation functions of operators using the light glueball states. The anisotropy of the theory yields different correlation functions for operators separated in the $x^1$ and $x^2$-directions.