Revisiting symmetries of lattice fermions via spin-flavor representation

TL;DR

This paper analyzes the symmetries and spontaneous symmetry breaking mechanisms in various lattice fermion formulations using the spin-flavor representation, revealing symmetry enhancements and their breakdown at specific parameters.

Contribution

It provides a unified analysis of doubler-mixing symmetries across multiple lattice fermion types using spin-flavor representation, highlighting symmetry enhancements and spontaneous breakdown mechanisms.

Findings

Naive fermion exhibits U(4)×U(4)A symmetries.

Wilson fermion has a U(1) symmetry that can be enhanced at specific mass values.

Minimally doubled fermions show similar symmetry enhancement and spontaneous breakdown.

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.