Topological Aspects of Fermions on Hyperdiamond

Abstract

Motivated by recent results on the index of the Dirac operator D=γ^{μ}D_{μ} of QCD on lattice and also by results on topological features of electrons and holes of 2-dimensional graphene, we compute in this paper the Index of D for fermions living on a family of even dimensional lattices denoted as L_{2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological Index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L_{2N} which are shown to be intimately linked with the weight lattices of SU(2N+1). The Index associated with the two leading N=1 and N=2 elements of this family describe precisely the chiral anomalies of graphene and QCD_4. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L_{2N} and applications to QCD_4 are also given.

LaTeX, 56 pages, 6 figures

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Cited by in corpus (7)

• Mathematical structure of three - dimensional (3D) Ising model
• Higher order topological matter and fractional chiral states
• On Flavor Symmetry in Lattice Quantum Chromodynamics
• On topological aspects of 2D graphene like materials
• Algebraic constructions of code lattices in Narain conformal field theories
• Twisted 3D $N=4$ Supersymmetric YM on deformed ${\mathbb{A}}_3^{\ast }$ Lattice
• Code CFTs and Topological Matter