# Non-Gaussian fixed point candidates in the 4D compact U(1) gauge theories

## TL;DR

This paper investigates nonperturbative properties of 4D compact U(1) lattice gauge theories, identifying non-Gaussian fixed points and phase transitions that suggest possible non-asymptotic free continuum limits, with implications for gauge theories and the Standard Model.

## Contribution

It demonstrates the existence of a non-Gaussian fixed point in pure gauge theory and explores phase transitions with matter fields, revealing new fixed points and dynamical symmetry breaking phenomena.

## Key findings

- Pure gauge theory has a non-Gaussian fixed point at the phase transition.
- Scalar matter fields exhibit Gaussian behavior at the Higgs transition endpoint.
- Presence of a tricritical point with dynamical fermion mass generation.

## Abstract

Some interesting nonperturbative properties of the strongly coupled 4D compact U(1) lattice gauge theories, both without and with matter fields, are pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed point with $\nu = 0.365(8)$ at the second order confinement-Coulomb phase transition. Thus a non-asymptotic free and nontrivial continuum limit of this theory, and of its various dual equivalents, in particular of a special case of the effective string theory, can be constructed. Including a scalar matter field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of the Higgs phase transition line. In the theory with both scalar and fermion matter fields, we demonstrate the existence of a tricritical point. Here, the chiral symmetry is broken, and the mass of unconfined composite fermions is generated dynamically. Appart from the Goldstone bosons, the spectrum contains also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling behavior is different from that in the NJL model and the nonperturbative renormalizability might thus be possible.