On Flavor Symmetry in Lattice Quantum Chromodynamics
arXiv:1203.6004 · doi:10.1063/1.3682640
Abstract
Using a well established method to engineer non abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al of refs [1,2] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of . We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form , are related with the small resolution of conifold singularity that live at . Other related features are also studied.
LaTex, 40 pages, 8 figures
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