Nicolai mapping versus exact chiral symmetry on the lattice

Abstract

The two-dimensional $N=2$ Wess-Zumino model is constructed on the lattice through Nicolai mapping with a Ginsparg-Wilson fermion. The Nicolai mapping requires a certain would-be surface term in the bosonic action which ensures the vacuum energy cancellation even on the lattice, but inevitably breaks chiral symmetry. With the Ginsparg-Wilson fermion, the holomorphic structure of the would-be surface term is maintained, leaving a discrete subgroup of the exact chiral symmetry intact for a monomial scalar potential. Through this feature both the boson and fermion can be kept massless on the lattice without any fine-tuning.