Four-dimensional graphene

Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in [P. F. Bedaque et al., Phys. Rev. D 78, 017502 (2008)] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H-4. We first study the link between the H-4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors lambda(1), lambda(2), lambda(3), lambda(4), and lambda(5) of the five-dimensional representation of SU(5) satisfying Sigma(i)lambda(i) = 0. After that, we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots alpha(1), alpha(2), alpha(3), and alpha(4) generating H-4; and its fundamental weights omega(1), omega(2), omega(3) omega(4) which generate the reciprocal lattice H-4*. It is shown, among others, that these zeros live at the sites of H-4(*); and the continuous limit D is given by id root 5/2 gamma(mu)k(mu) with d, gamma(mu), and k(mu) standing, respectively, for the lattice parameter of H-4, the usual 4 Dirac matrices and the 4D wave vector. Other features, such as differences with BBTW model as well as the link between the Dirac operator following from our construction and the one suggested by Creutz using quaternions, are also given.