Non-$\gamma_{5}$hermiticity fermions in two dimensions

TL;DR

This paper introduces a new class of two-dimensional fermions that break $\gamma_5$-hermiticity, analyzing their properties and applying them to the Gross-Neveu model to explore phase diagrams with broken symmetries.

Contribution

It constructs and studies non-$\gamma_5$-hermiticity fermions in 2D, providing insights into their symmetries and applications to phase diagram analysis.

Findings

Fermions exhibit specific eigenvalue distributions and pole structures.

Phase diagrams with parity and chiral symmetry breaking are mapped.

The fermions show potential for lattice gauge theory applications.

Abstract

We construct 2D non-$\gamma_{5}$hermiticity fermions based on the minimal doubling fermion. We investigate symmetries, reflection positivity, eigenvalue distribution and the number of poles for our fermions. As simple tests for application to the fermion, the Gross-Neveu model in two dimensions is studied using the non-$\gamma_{5}$hermiticity fermion. We draw the parity broken phase diagram, called Aoki phase and the chiral broken phase diagram for the model with an imaginary chemical potential.