Applying Integrability to Gauge Theories

TL;DR

This paper explores how lattice Yang-Mills theories can be understood as coupled integrable systems in lower dimensions, enabling exact calculations of physical quantities and revealing connections across different energy regimes.

Contribution

It introduces a novel approach applying integrability to gauge theories across various dimensions, including high-energy limits and renormalization techniques.

Findings

Exact quark-antiquark potential in 2+1 dimensions

Mass spectrum calculations using 1+1-dimensional S-matrix

High-energy anisotropic action derived in 3+1 dimensions

Abstract

Lattice Yang-Mills theories in any dimension may be regarded as coupled 1+1-dimensional integrable field theories. These integrable systems decouple at large center-of-mass energies, where the action becomes effectively anisotropic. This effective action is the high-energy center-of-mass limit of the gauge theory. In 2+1 dimensions, the quark-antiquark potential and the mass spectrum can be calculated, using the exact 1+1-dimensional S-matrix and form factors. The methods are quite similar to those applying integrability in statistical and condensed-matter physics. The high-energy anisotropic action at one loop in 3+1 dimensions has been found using a Wilsonian renormalization method. We briefly discuss the isotropic theory in 2+1 dimensions and the connection with soft scattering in 3+1 dimensions.