From Domain Wall to Overlap in 2+1d

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 $\frac{1}{2}(1\pm {\gamma }_3)$, 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.

Comments: 13 pages