On Dirac Zero Modes in Hyperdiamond Model

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 Ω_{μ}^{l} with 4\times5 complex components linking the Euclidean SO(4) vector μ; and the 5-dimensional representation of SU(5). The Boriçi-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of Ω_{μ}^{l}. Other features are also given. Keywords: Lattice QCD, Boriçi-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene, SU(5) Symmetry.

LaTex, 28 pages, To appear in Phys Rev D

References in corpus (9)

• The electronic properties of graphene
• Four-dimensional graphene and chiral fermions
• Creutz Fermions on an Orthogonal Lattice
• Broken Symmetries from Minimally Doubled Fermions
• Perturbative renormalization of lattice N=4 super Yang-Mills theory
• Electronic Properties and Hidden Symmetries of Graphene
• Search for Fermion Actions on Hyperdiamond Lattices
• Graphene, Lattice QFT and Symmetries
• Classification of Minimally Doubled Fermions

Cited by in corpus (12)

• Four Dimensional Graphene
• Phase structure for lattice fermions with flavored chemical potential terms
• QCD phase diagram with 2-flavor lattice fermion formulations
• Higher order topological matter and fractional chiral states
• Topological Aspects of Fermions on Hyperdiamond
• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Structural, electronic and topological properties of 3D TmBi compound
• On Flavor Symmetry in Lattice Quantum Chromodynamics
• Graphene, its Homologues and Their Classification
• Topological Properties of Bilayer $\alpha -T_3$ Lattice Induced by Polarized Light
• Code CFTs and Topological Matter
• Twisted 3D $N=4$ Supersymmetric YM on deformed ${\mathbb{A}}_3^{\ast }$ Lattice