Yang-Mills Theories as Deformations of Massive Integrable Models

TL;DR

This paper explores the connection between 2+1 dimensional Yang-Mills theories and integrable 1+1 dimensional principal chiral sigma models, providing new form factors, correlation functions, and insights into the spectrum and quantum corrections.

Contribution

It introduces explicit form factors and correlation functions for the principal chiral sigma model in large-N limit, extending previous SU(2) results to SU(N), and analyzes the quantum corrections in anisotropic gauge theories.

Findings

Calculated form factors and correlation functions for the sigma model.

Extended results from SU(2) to SU(N) in Yang-Mills theory.

Analyzed quantum corrections during the isotropic to anisotropic flow.

Abstract

Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. We calculate all the form factors and two-point correlation functions of the Noether current and energy-momentum tensor, in 't~Hooft's large-$N$ limit (some form factors can be found even at finite $N$). We use these new form factors to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results from Orland to $SU(N)$. The anisotropic gauge theory is related to standard isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in momentum. We calculate quantum corrections to the effective action of QED and QCD, as the theory flows from isotropic to anisotropic. The exact principal chiral sigma model S-matrix is also used to examine the spectrum of (1+1)-dimensional massive Yang Mills theory.