Nicolai mapping vs. exact chiral symmetry on the lattice

TL;DR

This paper explores the construction of the 2D N=2 Wess-Zumino model on the lattice using Nicolai mapping with Ginsparg-Wilson fermions, maintaining certain chiral symmetries and massless states without fine-tuning.

Contribution

It demonstrates how to preserve a discrete chiral symmetry subgroup and masslessness in lattice Wess-Zumino models using Nicolai mapping and Ginsparg-Wilson fermions.

Findings

Vacuum energy cancellation achieved on the lattice.

Chiral symmetry subgroup remains intact.

Boson and fermion remain massless without fine-tuning.

Abstract

Two-dimensional N=2 Wess-Zumino model is constructed on the lattice through Nicolai mapping with 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. By this feature both boson and fermion can be kept massless on the lattice without any fine-tuning.