Determinant of a new fermionic action on a lattice - (I)

TL;DR

This paper analyzes a new fermionic lattice action that preserves chiral symmetry and has a reduced number of components, demonstrating its determinant's positivity and reality for different gauge groups, which is promising for lattice gauge theories.

Contribution

It introduces a novel fermionic action on a lattice that maintains chiral symmetry and shows the fermion determinant's positivity for U(1) and SU(N) gauge groups.

Findings

Determinant is real and positive for U(1) gauge group under specific conditions.

Determinant is real and positive for SU(N) gauge group without additional conditions.

The new action preserves discrete chiral symmetry and reduces fermion components.

Abstract

We investigate, analytically and numerically, the fermion determinant of a new action on a (1+1)-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is a half of that of Kogut-Susskind. In particular, we show that our fermion determinant is real and positive for U(1) gauge group under specific conditions, which correspond to gauge conditions on the infinite lattice. It is also shown that the determinant is real and positive for SU(N) gauge group without any condition.