Note on the Lattice Fermion Chiral Symmetry Group

Abstract

The group structure of the variant chiral symmetry discovered by Luscher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of the chiral group, and the CP transformation properties of the symmetry generators is found. Features of the currents associated with these symmetries are discussed, including the fact that some different, non-commuting symmetry generators lead to the same Noether current. These strange features occur in all implementations of lattice fermions based on the Ginsparg-Wilson relation, including overlap, domain-wall, and perfect-action chiral fermions. The conclusions are illustrated in a solvable example, free overlap fermions.

20 pages, pdf format only. All conclusions are unchanged. Material has been added and rearranged to clarify the logic of the arguments. References added

Cited by in corpus (8)

• A renormalisation group derivation of the overlap formulation
• Symmetries of Ginsparg-Wilson Chiral Fermions
• A Ginsparg-Wilson approach to lattice CP symmetry, Weyl and Majoranna fermions, and the Higgs mechanism
• Block renormalization group transformations and overlap fermions
• A Ginsparg-Wilson approach to lattice $\mathcal{C}\mathcal{P}$ symmetry
• A further extension to the group of Ginsparg-Wilson (overlap) chiral symmetries
• The conserved axial current in the presence of multiple chiral symmetries
• Anomaly at finite density and chiral fermions on lattice