Revisiting symmetries of lattice fermions via spin-flavor representation

Abstract

Employing the spin-flavor representation, we investigate the structures of the doubler-mixing symmetries and the mechanisms of their spontaneous breakdown in four types of lattice fermion formulation. We first revisit the \(U(4)\timesU(4)A\) symmetries of the naive fermion with the vanishing bare mass m, and re-express them in terms of the spin-flavor representation. We apply the same method to the Wilson fermion, which possesses only the U(1) vector symmetry for general values of m. For a special value of m, however, there emerges an additional U(1) symmetry to be broken by pion condensation. We also explore two types of minimally doubled fermion, and discover a similar kind of symmetry enhancement and its spontaneous breakdown.