Fermion Determinants: Some Recent Analytic Results

TL;DR

This paper proposes using known continuum fermion determinants as benchmarks to verify the universality hypothesis in lattice QCD and QED, aiding the extrapolation to zero lattice spacing.

Contribution

It introduces a method to utilize analytic continuum results as benchmarks for lattice fermion determinant extrapolations, testing universality across different fermion discretizations.

Findings

Continuum fermion determinants can serve as effective benchmarks.

The approach helps verify the universality hypothesis in lattice fermion formulations.

Provides a framework for more accurate zero lattice spacing extrapolations.

Abstract

The use of known analytic results for the continuum fermion determinants in QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice fermion determinants is proposed. Specifically, they can be used as a check on the universality hypothesis relating the continuum limits of the na\"{\i}ve, staggered and Wilson fermion determinants.