Overlap-Dirac fermions with a small hopping parameter

TL;DR

This paper investigates the phase structure of overlap-Dirac fermions at small hopping parameters, proving the existence of a symmetry-preserving phase and conjecturing the overall phase diagram for these theories.

Contribution

It provides a rigorous proof of a symmetry-preserving phase at large positive M and proposes a conjecture for the phase diagram of overlap-Dirac fermions in gauge theories.

Findings

Existence of a phase with unbroken $U_A(1)$ symmetry at large positive M.

The pseudo-scalar becomes an exact Goldstone boson in this phase.

A conjectured phase diagram for asymptotically free gauge theories with overlap-Dirac fermions.

Abstract

We consider overlap-Dirac fermions at non-zero bare coupling and for a small hopping parameter, or, equivalently, large $|M|$ with $M$ the domain-wall height. We prove the existence of a phase at large positive $M$ where the abelian axial group $U_A(1)$ is a symmetry, and the corresponding pseudo-scalar is an exact Goldstone boson. We also provide a conjecture for the phase diagram of asymptotically free gauge theories with overlap-Dirac fermions. In particular, we suggest that, for large gauge coupling, the massive-fermion phase at negative $M$ possibly extends to all $M<4$.