Topological susceptibility in full QCD with Ginsparg-Wilson fermions

TL;DR

This paper demonstrates a precise lattice definition of topological susceptibility in full QCD using Ginsparg-Wilson fermions, enabling unambiguous calculations at finite quark masses without divergent subtractions.

Contribution

It introduces a new lattice formulation for topological susceptibility in full QCD that is both precise and free of power divergences, improving upon previous methods.

Findings

Lattice expression for chi_tL matches continuum form

No power divergent subtractions needed for chi_tL

Enables direct, multiplicative renormalization of chiral condensate

Abstract

We show that, if the formula for the topological charge density operator suggested by fermions obeying the Ginsparg-Wilson relation is employed, it is possible to give a precise and unambiguous definition of the topological susceptibility in full QCD, chi_tL, for finite quark masses on the lattice. The lattice expression of chi_tL looks like the formal continuum one, in the sense that no power divergent subtractions are needed for its proper definition. As a consequence, the small mass behaviour of chi_tL leads directly to a multiplicative renormalizable definition of the chiral condensate that does not require any power divergent subtraction.