On flavor symmetry in lattice quantum chromodynamics

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. [PoS: Lattice 2010, 078 (2010) and Creutz et al. JHEP 041, 1012 (2010)] 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 QCD2N, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of [SU(2)]2N. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form \documentclass[12pt]{minimal}\begin{document}$i\mathbf {\gamma }_{1}\mathrm{F}_{1}+i\mathbf {\gamma }_{2}\mathrm{F}_{2}+ i\mathbf {\gamma }_{3}\mathrm{F}_{3}+ \frac{i}{\sin \alpha }\mathbf {\gamma }_{^{4}}\mathrm{F}_{4}$\end{document}iγ1F1+iγ2F2+iγ3F3+isinαγ4F4, are related with the small resolution of conifold singularity that live at sin α = 0. Other related features are also studied.