Solving 3+1 QCD on the Transverse Lattice Using 1+1 Conformal Field Theory

TL;DR

This paper introduces a novel transverse lattice model for 3+1 QCD that leverages conformal field theory and Wess-Zumino terms to exactly solve link dynamics, offering a promising framework for non-perturbative QCD studies.

Contribution

It constructs a new solvable transverse lattice model for 3+1 QCD using Wess-Zumino terms and non-Abelian current algebra, avoiding linear approximations of the sigma model.

Findings

Preserves non-perturbative sigma model behavior.

Eliminates need for linear sigma model approximation.

Provides a framework for analytic non-perturbative QCD studies.

Abstract

A new transverse lattice model of $3+1$ Yang-Mills theory is constructed by introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to solve the basic non-linear sigma model dynamics of each link, for discrete values of the bare QCD coupling constant, by applying the representation theory of non-Abelian current (Kac-Moody) algebras. This construction eliminates the need to approximate the non-linear sigma model dynamics of each link with a linear sigma model theory, as in previous transverse lattice formulations. The non-perturbative behavior of the non-linear sigma model is preserved by this construction. While the new model is in principle solvable by a combination of conformal field theory, discrete light-cone, and lattice gauge theory techniques, it is more realistically suited for study with a Tamm-Dancoff truncation of excited states. In this context, it may serve as a useful framework for the study of non-perturbative phenomena in QCD via analytic techniques.