A Schur Complement Approach to Chiral Fermions

TL;DR

This paper introduces a Schur complement-based renormalization group method for lattice chiral fermions, enabling improved coarse lattice fermion formulations while maintaining gauge fields on fine lattices, with numerical validation in lattice QCD.

Contribution

It presents a novel RG approach using Schur complements to construct highly improved chiral fermions on coarse lattices in lattice QCD.

Findings

Stable and regular Schur complement approximation enables iteration to fixed points.

Numerical examples demonstrate improved chiral fermions in lattice QCD.

Gauge fields remain on fine lattices while fermions are coarse-grained.

Abstract

Lattice chiral fermions are synonymous to the Ginsparg-Wilson relation. Indeed, this relation is satisfied by the overlap, domain wall and perfect action fermion kernel. In a recent work we have shown that it is possible to take a direct RG approach for fermions in the presence of gauge fields. This is due to an algebraically implicit blocking technique which yields a Schur-complementary coarse Dirac operator. Using a Schur complement approximation which is stable and regular, the scheme can be iterated to the fixed point. In this talk, we elaborate more on the direct RG approach and show how to get highly improved chiral fermions on the coarse lattice with the gauge fields remaining on the fine lattice. We give numerical examples in the case of lattice QCD using QCDLAB {\tt http://phys.fshn.edu.al/qcdlab.html}