The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing

TL;DR

This paper examines the challenges of the rooting trick in lattice fermion formulations, demonstrating that a simplified two-flavor model with exact chiral symmetries still exhibits issues similar to those identified by Creutz, raising questions about the trick's validity.

Contribution

The study introduces a simplified two-flavor lattice fermion model with no taste mixing but with chiral symmetries, and shows it still faces rooting issues similar to more complex formulations.

Findings

Presence of robust zero-modes in topologically nontrivial backgrounds

Rooted determinant correctly reflects zero-modes and U(1) problem

Model likely in the correct universality class for QCD

Abstract

To investigate the viability of the 4th root trick for the staggered fermion determinant in a simpler setting, we consider a two taste (flavor) lattice fermion formulation with no taste mixing but with exact taste-nonsinglet chiral symmetries analogous to the taste-nonsinglet $U(1)_A$ symmetry of staggered fermions. M. Creutz's objections to the rooting trick apply just as much in this setting. To counter them we show that the formulation has robust would-be zero-modes in topologically nontrivial gauge backgrounds, and that these manifest themselves in a viable way in the rooted fermion determinant and also in the disconnected piece of the pseudoscalar meson propagator as required to solve the U(1) problem. Also, our rooted theory is heuristically seen to be in the right universality class for QCD if the same is true for an unrooted mixed fermion action theory.