Minimally Truncated SU(3) Lattice Gauge Theory and String Tension

TL;DR

This paper investigates SU(3) lattice gauge theory using a minimal electric field truncation on small lattices, providing explicit Hamiltonian formulations, spectrum analysis, and string tension calculations, with implications for understanding confinement and screening.

Contribution

It introduces a minimally truncated SU(3) lattice gauge theory formalism with explicit Hamiltonian expressions and applies it to compute spectra and string tensions on small lattices.

Findings

Exact diagonalization yields the gauge field energy spectrum.

Computed SU(3) string tension and its modification by vacuum fluctuations.

Analyzed static quark potentials and screening effects at finite temperature.

Abstract

We study SU(3) gauge theory on small lattices in the minimal (qutrit) electric field truncation retaining only the ${\bf 1}, {\bf 3}, {\bf \overline{3}}$ representations for the link variables. Explicit expressions are given for the Kogut-Susskind Hamiltonian for the square plaquette chain and the two-dimensional honeycomb lattice. Our formalism can be easily extended to the minimally truncated general SU($N_c$) gauge theory. The addition of (static) quarks is discussed. We present results for the energy spectrum of the gauge field on these lattices by exact diagonalization of the Hamiltonian and analyze its statistical properties. We also compute the SU(3) string tension and discuss how it is modified by vacuum fluctuations. Finally, we calculate the potential energies of a static quark-antiquark pair and three static quarks and study their screening at finite temperature.