Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices

TL;DR

This paper extends various fermion actions on hyperdiamond lattices to higher dimensions, analyzing their properties, limitations, and introducing new classes like Appended Creutz actions, highlighting increased difficulty in maintaining minimal-doubling as dimensions grow.

Contribution

It generalizes fermion actions to higher dimensions, identifies limitations, and introduces new classes such as Appended Creutz actions, advancing understanding of lattice fermions in higher-dimensional spaces.

Findings

Higher-dimensional BBTW fermions have unphysical degrees of freedom.

Creutz fermions lose symmetry on distorted lattices in higher dimensions.

The parameter range for minimal-doubling decreases with increasing dimension.

Abstract

In this paper we generalize to higher dimensions several types of fermion actions on the hyperdiamond lattice including a two-parameter class of minimal-doubling fermions "Creutz fermion" and a simple fermion with sufficient discrete symmetry "BBTW fermion". Then it is shown that they possess some properties in common with the four-dimensional case: BBTW fermions in higher even dimensions inevitably yield unphysical degrees of freedom. Creutz fermions are defined on the distorted lattices, and they lose the high discrete symmetry of the original lattices. We also find properties specific to the higher-dimensional cases. The parameter range for Creutz action to yield minimal-doubling and physical fermions becomes narrower with the dimension getting higher, thus it becomes more and more difficult to realize minimal-doubling. In addition, we generalize the subspecies of Creutz and BBTW actions including a new class of minimal-doubling actions "Appended Creutz action".