Pion mass and the PCAC relation in the overlap fermion formalism: Gauged Gross–Neveu model on a lattice

We investigate chiral properties of the overlap lattice fermion by using solvable model in two dimensions, the gauged Gross–Neveu model. In this model, the chiral symmetry is spontaneously broken in the presence of small but finite fermion mass. We calculate the quasi-Nambu–Goldstone (NG) boson mass as a function of the bare fermion mass and two parameters in the overlap formula. We find that the quasi-NG boson mass has desired properties as a result of the extended chiral symmetry found by Lüscher. We also examine the PCAC relation and find that it is satisfied in the continuum limit. Comparison between the overlap and Wilson lattice fermions is made.