Mass gap in compact U(1) Model in (2+1) dimensions

TL;DR

This paper presents a numerical study of the mass gap in the (2+1)-dimensional compact U(1) lattice gauge theory, confirming theoretical predictions and comparing with previous Hamiltonian results.

Contribution

It provides the first detailed Monte Carlo analysis of the antisymmetric mass gap scaling in this model, validating asymptotic predictions and extrapolating to the Hamiltonian limit.

Findings

Evidence of scaling behaviour in the antisymmetric mass gap

Results consistent with G{" o}pfert and Mack's asymptotic form

Comparison with previous Hamiltonian estimates

Abstract

A numerical study of low-lying glueball masses of compact U(1) lattice gauge theory in (2+1) dimensions is performed using Standard Path integral Monte Carlo techniques. The masses are extracted, at fixed (low) temperature, from simulations on anisotropic lattices, with temporal lattice spacing much smaller than the spatial ones. Convincing evidence of the scaling behaviour in the antisymmetric mass gap is observed over the range $1.4<\beta <2.25$. The observed behaviour is very consistent with asymptotic form predicted by G{\" o}pfert and Mack. Extrapolations are made to the "Hamiltonian" limit, and the results are compared with previous estimates obtained by many other Hamiltonian studies.