Domain-wall fermions with $U(1)$ dynamical gauge fields

TL;DR

This paper presents a numerical simulation of a (2+1)-dimensional domain-wall model with a dynamical gauge field in an extra dimension, exploring phase transitions and zero mode existence relevant for lattice chiral gauge theories.

Contribution

It demonstrates the existence of a critical domain-wall mass separating phases with and without fermionic zero modes, supporting the viability of domain-wall methods for chiral gauge theories.

Findings

Existence of a critical domain-wall mass $m_0^c$

Zero modes present below $m_0^c$

Potential for lattice chiral gauge theory construction

Abstract

We have carried out a numerical simulation of a domain-wall model in $(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a ( 2-dimensional ) physical gauge coupling. Using a quenched approximation we have investigated this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase), 1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. We have found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain-wall from the one without it, in both symmetric and broken phases. This result suggests that the domain-wall method may work for the construction of lattice chiral gauge theories.