A different kind of continuum limit for the three-dimensional U(1) gauge theory
Abstract
In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter μ. By tuning β and μ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing β, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.
Related
- Growth of helicity in salt-finger convection in the two-dimensional three-component limit
- Low-threshold vortex lasing in three-dimensional cavities via flatband bound states in the continuum
- Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
- Emergent dynamical scaling in the inviscid limit of three-dimensional stochastic Navier–Stokes equation with thermal noise
- Octupole deformation in even-even Ra isotopes from covariant density functional theory with localized exchange terms in a three-dimensional lattice space
BibTeX
@misc{athenodorou2026different,
title = {{A different kind of continuum limit for the three-dimensional U(1) gauge theory}},
author = {Andreas Athenodorou and Claudio Bonati and Ivan Soler Calero},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.27976},
eprint = {2608.27976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27976},
}
RIS
TY - UNPB
TI - A different kind of continuum limit for the three-dimensional U(1) gauge theory
AU - Andreas Athenodorou
AU - Claudio Bonati
AU - Ivan Soler Calero
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.27976
UR - https://arxiv.org/abs/2608.27976
AB - In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter μ. By tuning β and μ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing β, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.
ER -