A simplified test of universality in Lattice QCD

TL;DR

This paper investigates the universality in Lattice QCD by analytically comparing fermion determinants in continuous Euclidean time limits, revealing a gauge field-dependent anomaly that challenges expected universality relations.

Contribution

It introduces a simplified analytical test for universality in Lattice QCD and uncovers a gauge field-dependent anomaly in fermion determinant relations.

Findings

Discovered a gauge field-dependent factor violating expected determinant relations

Uncovered a 'universality anomaly' in the continuous Euclidean time limit

Highlights the need to understand the physical significance of the anomaly

Abstract

A simplified test of universality in Lattice QCD is performed by analytically evaluating the continuous Euclidean time limits of various lattice fermion determinants, both with and without a Wilson term to lift the fermion doubling on the Euclidean time axis, and comparing them with each other and with the zeta-regularised fermion determinant in the continuous time--lattice space setting. The determinant relations expected from universality considerations are found to be violated by a certain gauge field-dependent factor, i.e. we uncover a "universality anomaly". The physical significance, or lack thereof, of this factor is a delicate question which remains to be settled.