From Domain Wall to Overlap in 2+1d

TL;DR

This paper demonstrates the equivalence of domain wall and overlap fermion formulations in 2+1D lattice gauge theories, analyzing symmetry properties and finite separation effects to improve understanding of chiral symmetry realization.

Contribution

It establishes the equivalence between domain wall and overlap fermions in 2+1D, detailing symmetry behaviors and finite separation corrections in lattice gauge theories.

Findings

Finite-$L_s$ overlap operator is invariant under interchange of $\gamma_3$ and $\gamma_5$.

Ginsparg-Wilson relations recover expected symmetry in the limit $L_s o\infty$.

Finite-$L_s$ corrections depend on the presence of even powers of the symmetry-breaking mass.

Abstract

The equivalence of domain wall and overlap fermion formulations is demonstrated for lattice gauge theories in 2+1 spacetime dimensions with parity-invariant mass terms. Even though the domain wall approach distinguishes propagation along a third direction with projectors ${1\over2}(1\pm\gamma_3)$, the truncated overlap operator obtained for finite wall separation $L_s$ is invariant under interchange of $\gamma_3$ and $\gamma_5$. In the limit $L_s\to\infty$ the resulting Ginsparg-Wilson relations recover the expected U($2N_f$) global symmetry up to O($a$) corrections. Finally it is shown that finite-$L_s$ corrections to bilinear condensates associated with dynamical mass generation are characterised by whether even powers of the symmetry-breaking mass are present; such terms are absent for antihermitian bilinears such as $i\bar\psi\gamma_3\psi$, markedly improving the approach to the large-$L_s$ limit.