(2+1)-dimensional Yang-Mills theory and form factor perturbation theory

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 $SU(N)\ifmmode\times\else\texttimes\fi{}SU(N)$ 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.