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+12+1 spacetime dimensions with parity-invariant mass terms. Even though the domain wall approach distinguishes propagation along a third direction with projectors 12(1±γ3), the truncated overlap operator obtained for finite wall separation LsLs is invariant under interchange of γ3γ3 and γ5γ5. In the limit Ls→∞Ls→∞ the resulting Ginsparg–Wilson relations recover the expected U(2Nf)U(2Nf) global symmetry up to O(a)O(a) corrections. Finally it is shown that finite-LsLs 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 iψ¯γ3ψ, markedly improving the approach to the large-LsLs limit.