# Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice

## TL;DR

This paper provides numerical evidence for a non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory, indicating the possibility of a nontrivial continuum limit with potential implications for related models.

## Contribution

It demonstrates the existence of a non-Gaussian fixed point in 4D U(1) gauge theory through high-precision lattice simulations, suggesting a nontrivial continuum limit.

## Key findings

- Second-order phase transition line including Wilson action
- Fixed point with non-Gaussian critical exponent nu=0.365(8)
- Implications for related models like monopole gas and Higgs model

## Abstract

The line of phase transitions, separating the confinement and the Coulomb phases in the four-dimensional pure compact U(1) gauge theory with extended Wilson action, is reconsidered. We present new numerical evidence that a part of this line, including the original Wilson action, is of second order. By means of a high precision simulation on homogeneous lattices on a sphere we find that along this line the scaling behavior is determined by one fixed point with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the existence of a nontrivial and nonasymptotically free four-dimensional pure U(1) gauge theory in the continuum very probable. The universality and duality arguments suggest that this conclusion holds also for the monopole loop gas, for the noncompact abelian Higgs model at large negative squared bare mass, and for the corresponding effective string theory.