Truncated Overlap Fermions

After many years of research in lattice QCD, it was possible to formulate QCD with chiral fermions on the lattice [1–4]. The basic idea is an expanded flavor space which may be seen as an extra dimension with left and right handed fermions defined in the two opposite boundaries or walls. Let N be the size of the extra dimension, DW the Wilson-Dirac operator, and m the bare fermion mass. Then, the theory with Domain Wall Fermions is defined by the action [1,2]: SDW := Ψ̄MΨ = ∑N i=1 ψ̄i[(D || − 1)ψi +P+ψi+1 + P−ψi−1], P+(ψN+1 +mψ1) = 0, P−(ψ0 +mψN ) = 0 (1)