Transverse Lattice Approach to Light-Front Hamiltonian QCD

TL;DR

This paper develops a non-perturbative light-front Hamiltonian approach using a transverse lattice for SU(N) gauge theories, successfully predicting glueball masses and potentials in 2+1 dimensions that agree with Euclidean lattice results.

Contribution

It introduces a novel transverse lattice method with color-dielectric fields for solving light-front QCD and demonstrates its effectiveness in 2+1 dimensions, paving the way for 3+1-dimensional applications.

Findings

Predicted glueball masses agree with Euclidean lattice results.

Identified a scaling trajectory ensuring Lorentz covariance.

Calculated heavy source potentials and glueball structures.

Abstract

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the potential between heavy sources and the structure of the glueballs from their light-front wavefunctions. Finally, we briefly discuss the extension of these calculations to 3+1-dimensions.