Chirally improved Dirac operators: Studying the sensitivity to topological excitations for zero and finite temperature

TL;DR

This paper investigates the properties of a chirally improved lattice Dirac operator, examining its eigenmodes in instanton backgrounds and thermalized configurations to understand chiral symmetry breaking and topological effects in QCD.

Contribution

It introduces an approximate solution to the Ginsparg-Wilson equation and compares its behavior with other Dirac operators in various gauge backgrounds.

Findings

Eigenmodes reflect topological structures like instantons

Chiral symmetry breaking is linked to instantons

Results align with other Dirac operators' findings

Abstract

We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton backgrounds as well as for thermalized gauge configurations on both sides of the QCD phase transition. We compare with results from other Dirac operators including the overlap operator. The results support the picture of chiral symmetry breaking being closely related to instantons.