On Dirac Zero Modes in Hyperdiamond Model

TL;DR

This paper explores the structure of Dirac zero modes in 4D hyperdiamond lattice models, revealing a unifying tensor framework that encompasses existing models like Bori extc{c}i-Creutz and Karsten-Wilzeck.

Contribution

It introduces a tensor-based approach to characterize Dirac zero modes in 4D hyperdiamond fermions, unifying various lattice QCD models within a common framework.

Findings

Zero modes are described by a tensor with complex components linking SO(4) and SU(5).

Bori extc{c}i-Creutz and Karsten-Wilzeck models are special cases of this tensor framework.

The approach provides new insights into the symmetry structure of 4D lattice fermions.

Abstract

Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of 4D graphene given in "Four Dimensional Graphene" (L.B Drissi, E.H Saidi, M. Bousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice QCD fermions whose Dirac operators have two zero modes. We show that generally the zero modes of the Dirac operator in hyperdiamond fermions are captured by a tensor {\Omega}_{{\mu}}^{l} with 4\times5 complex components linking the Euclidean SO(4) vector {\mu}; and the 5-dimensional representation of SU(5). The Bori\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of {\Omega}_{{\mu}}^{l}. Other features are also given. Keywords: Lattice QCD, Bori\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene, SU(5) Symmetry.