New fermion discretizations and their applications

TL;DR

This paper reviews recent advances in novel lattice fermion formulations, highlighting their potential to improve computational efficiency and understanding in lattice field theory.

Contribution

It introduces and discusses three new types of lattice fermions—flavored-mass, central-branch Wilson, and minimally doubled fermions—and explores their advantages and implications.

Findings

Flavored-mass fermions can reduce numerical costs in overlap fermions.

Central-branch Wilson fermions avoid fine-tuning by forbidding additive mass renormalization.

Minimally doubled fermions achieve ultra-local chiral fermions with reduced species.

Abstract

We review the recent progress in new lattice fermion formulations. We focus on the following three types which have possibility of improving lattice simulations. (1) Flavored-mass fermions are a generalization of Wilson fermions with species-splitting mass terms. In particular, staggered-Wilson fermions initiated by Adams have possibilities of reducing numerical costs in overlap fermions and the influence of taste-breaking in staggered fermions. (2) Central-branch Wilson fermions, in which additive mass renormalization is forbidden by extra axial symmetry, could enable us to perform Wilson-fermion lattice QCD without fine-tuning. (3) Minimally doubled fermions, which reduce the number of species by species-dependent chemical potential terms, realizes a ultra-local chiral fermion at the price of hypercubic symmetry. These setups reveal unknown aspects of lattice fermions, and we obtain a deeper understanding of lattice field theory.