A Critical Surface of Chiral-invariant System with Gauge Boson and Fermions

TL;DR

This paper investigates the behavior of fermion self-energy in a chirally-invariant gauge system using lattice methods, identifying a critical surface that aligns with continuum theory predictions.

Contribution

It introduces a lattice analysis of the Schwinger-Dyson equation in a chiral gauge context, revealing a critical surface consistent with continuum results.

Findings

A well-defined infrared limit exists on a critical surface.

The critical surface matches the critical line in continuum theory.

Provides lattice evidence supporting continuum predictions.

Abstract

In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and four-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson equation for the fermion self-energy function is studied on a lattice. We find that a sensible infrared limit can be defined on a critical surface, which is consistent with the critical line found in the continuum theory.