Remarks on left-handed lattice fermions

TL;DR

This paper investigates the construction of left-handed lattice fermions, analyzing symmetry and anomaly manifestation through RG transformations and blocking from continuum, offering new insights into lattice fermion formulations.

Contribution

It introduces a novel formalism for deriving lattice actions from continuum fermions and characterizes lattice symmetries without relying solely on lattice projectors.

Findings

Derived equations characterizing lattice symmetries for left-handed fermions

Analyzed how continuum symmetries manifest on the lattice

Identified parameter regimes corresponding to left-handed continuum fermions

Abstract

We study whether applying lattice projectors on a vector-like Ginsparg-Wilson Dirac operator is the only way to construct left-handed lattice fermions. Using RG transformations we derive an equation for the generating functional on the lattice, obtained by blocking from the continuum. We analyze how symmetries of the continuum theory manifest themselves in this lattice generating functional and how anomalies emerge. The formalism is applied to left-handed continuum fermions and we derive two equations that characterize the corresponding lattice symmetries. To analyze possible solutions, we directly block a parameterized action for free continuum fermions to obtain the corresponding lattice action. Subsequently we study parameter values where the continuum action corresponds to left-handed fermions.