Zero density heavy quark SU(2) gauge theory and the Stefan-Boltzmann limit

TL;DR

This paper explores a constrained SU(2) lattice gauge theory where heavy quark density is zero, comparing its properties to pure SU(2) gauge theory and analyzing the static quark potential at zero temperature.

Contribution

It introduces a zero-density heavy quark SU(2) gauge theory and demonstrates its static potential matches pure SU(2) gauge theory, recovering known lattice behaviors.

Findings

Constrained theory's potential matches pure SU(2) gauge theory.

Lattice spacing behavior with beta is consistent with standard results.

Heavy quark density constraint does not alter the static potential.

Abstract

SU(2) lattice gauge theory is investigated where the traces of the Wilson lines at any lattice point and along each direction is constrained to zero. Hence, each of the lattice configurations possesses a vanishing density of heavy (anti-) quarks. The results are compared with those of pure SU(2) gauge theory which can be interpreted as the grand canonical realization of the heavy quark theory where only the ensemble average of the heavy quark density vanishes. The static quark anti-quark potential of the constrained theory is obtained from (spatially smeared) Wilson loops at zero temperature. We find that the potential coincides with that of pure SU(2) gauge theory (without constraints). Hence, the familiar "running" of the lattice spacing with beta is recovered.