Chiral gauged fermions on a lattice

TL;DR

This paper presents a lattice model for chiral fermions that preserves chiral gauge symmetry at low energies, correctly reproduces gauge anomalies, and maintains gauge invariance through a novel renormalization scheme.

Contribution

It introduces a lattice chiral fermion model with local multifermion interactions that successfully captures chiral gauge symmetry and anomalies, providing a consistent framework for continuum limit analysis.

Findings

Massless fermion remains chiral-gauged at low energy

15 massive Dirac fermions are vectorially gauged at lattice scale

Correct gauge anomaly and fermion-flavour anomalies are reproduced

Abstract

The chiral fermion model with local multifermion interactions proposed in Nucl. Phys. B486 (1997) 282 and Phys. Rev. D61 (2000) 054502 processes an exact SU_L(2) chiral gauge symmetry and SU_L(2) by U_R(1) chiral flavour symmetry on a lattice and a plausible scaling region for the target chiral gauge theory in the continuum limit. Following the previous analysis of massive and massless fermion spectra in the scaling region, we compute the coupling vertices between gauge field and fermions by the strong multifermion coupling expansion and analytical continuation of these vertex functions in the energy-momentum space. We show a peculiar scenario that a massless fermion is SU_L(2)-chirally gauged in the low energy and 15 non-degenerate massive Dirac fermions are SU_L(2)-vectorially gauged at the lattice scale O(1/a). The Ward identities associated to the chiral gauge symmetry are realized by both the massless chiral fermion and massive Dirac fermions. These Ward identities protect the perturbative calculations in the small gauge coupling from hard gauge-symmetry breakings and lead to the normal gauge-invariant renormalization prescription. The vacuum functional is perturbatively computed by a continuum regularization scheme in 16 edges of Brillouin zones. We achieve the correct form of the gauge anomaly and U_L(1) fermion-flavour singlet anomaly with the soft chiral symmetry breaking scale that is much smaller than the lattice scale. The residual breakings of chiral gauge symmetry after the gauge anomaly cancellation are eliminated in the normal gauge-invarinant renormalization prescription. We discuss the consistency of the scenario and the reasons for it to work for perturbative and non-perturbative gauge field.