Revisiting symmetries of lattice fermions via spin-flavor representation

Details Revisiting symmetries of lattice fermions via spin-flavor representation Revisiting symmetries of lattice fermions via spin-flavor representation

2011-11-02

arxiv.org/abs/1111.0402v3

JHEP 01 (2012) 048

Physics

High Energy Physics

High Energy Physics - Lattice

25 pages, no figure;v2 typos corrected;v3 Sec.2 is shortened. To appear in JHEP

Scientific paper

10.1007/JHEP01(2012)048

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.

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