# Non-compact Lattice QED with Two Charges: Phase Diagram and Renormalization Group Flow

## TL;DR

This paper studies the phase diagram and renormalization group flow of non-compact lattice QED with two different charges, revealing a validity bound for the theory and implications for the Standard Model at high energies.

## Contribution

It provides the first detailed analysis of the phase structure and renormalization flow in a non-compact lattice QED with multiple charges, including implications for fundamental physics.

## Key findings

- Renormalized charges agree with perturbation theory.
- No continuum limit with non-zero renormalized gauge coupling.
- A bound on the renormalized coupling at the Planck scale.

## Abstract

The phase diagram of non-compact lattice QED in four dimensions with staggered fermions of charges 1 and $-1/2$ is investigated. The renormalized charges are determined and found to be in agreement with perturbation theory. This is an indication that there is no continuum limit with non-vanishing renormalized gauge coupling, and that the theory has a validity bound for every finite value of the renormalized coupling. The renormalization group flow of the charges is investigated and an estimate for the validity bound as a function of the cut-off is obtained. Generalizing this estimate to all fermions in the Standard Model,it is found that a cut-off at the Planck scale implies that $\alpha_R$ has to be less than $1/80$. Due to spontaneous chiral symmetry breaking, strongly bound fermion-antifermion composite states are generated. Their spectrum is discussed.