SU(N) Lattice Gauge Theory on a Single Cube

TL;DR

This paper explores analytic variational methods for calculating glueball masses in 3+1 dimensional lattice gauge theory, using a simplified single-cube model to identify promising scaling behaviors.

Contribution

It develops analytic techniques to approximate integrals in 3+1D variational glueball mass calculations and applies them to a single-cube lattice model.

Findings

Signs of approach to asymptotic scaling for SU(N) 1^{+-} glueball mass as N increases.

Successful development of analytic approximation methods for complex integrals in 3+1D LGT.

Demonstration of potential for simplified models to inform understanding of glueball spectra.

Abstract

In this paper we study the viability of persuing analytic variational techniques for the calculation of glueball masses in 3+1 dimensional Hamiltonian lattice gauge theory (LGT) in the pure gauge sector. We discuss the major problems presented by a move from 2+1 to 3+1 dimensions and develop analytic techniques to approximate the integrals appearing in 3+1 dimensional variational glueball mass calculations. We calculate $0^{++}$ and $1^{+-}$ glueball masses on a lattice consisting of a single cube. Despite the use of a very simplistic model, promising signs of an approach to asymptotic scaling is displayed by the SU(N) $1^{+-}$ glueball mass as N is increased.