Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions

TL;DR

This paper uses Path Integral Monte Carlo simulations to study U(1) lattice gauge theory in (2+1) dimensions, analyzing static potentials, string tension, and glueball spectrum, confirming some theoretical predictions while noting magnitude discrepancies.

Contribution

It applies Path Integral Monte Carlo to U(1) lattice gauge theory in (2+1)D, providing new numerical estimates and comparisons with Hamiltonian formulation results.

Findings

Euclidean string tension and mass gap decrease exponentially at weak coupling.

Magnitudes of string tension and mass gap are five times larger than theoretical predictions.

Extrapolations to anisotropic and Hamiltonian limits are performed and compared.

Abstract

Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static quark potential, the string tension and the low-lying "glueball" spectrum.The Euclidean string tension and mass gap decrease exponentially at weakcoupling in excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.