From Domain Wall to Overlap in 2+1d

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 ${1\over2}(1\pmγ_3)$, the truncated overlap operator obtained for finite wall separation $L_s$ is invariant under interchange of $γ_3$ and $γ_5$. 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 $i\barψγ_3ψ$, markedly improving the approach to the large-$L_s$ limit.

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