Analytical Formulae linking Quark Confinement and Chiral Symmetry Breaking

Takahiro M Doi,Chihiro Sasaki,Hideo Suganuma,Krzysztof Redlich,L Bravina,Y Foka,S Kabana

doi:10.1051/epjconf/201612604016

Abstract

Dirac spectrum representations of the Polyakov loop fluctuations are derived on the temporally odd-number lattice, where the temporal length is odd with the periodic boundary condition. We investigate the Polyakov loop fluctuations based on these analytical relations. It is semi-analytically and numerically found that the low-lying Dirac eigenmodes have little contribution to the Polyakov loop fluctuations, which are sensitive probe for the quark deconfinement. Our results suggest no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD.

Highlights

It is one of the most important problems in particle and nuclear physics to understand the nonperturbative properties of QCD, such as confinement and chiral symmetry breaking, including these relation
The low-lying eigenmodes of the Dirac operator are important for chiral symmetry breaking, for example known as Banks-Casher relation [3]
Known as the Banks-Casher relation [3], the low-lying Dirac modes have the dominant contribution to the chiral condensate ψψ and these modes are essential modes for chiral symmetry breaking

Summary

Introduction

It is one of the most important problems in particle and nuclear physics to understand the nonperturbative properties of QCD, such as confinement and chiral symmetry breaking, including these relation. In the presence of light dynamical quarks, both quark deconfinement and chiral restoration are not phase transition but crossover and take place in the same temperature region [4,5,6,7] This observation seems evidence that confinement and chiral symmetry breaking are strongly correlated in QCD. We semi-analytically and numerically show that low-lying Dirac modes have negligible contribution to the Polyakov loop fluctuations based on these analytical relations. This talk is mainly based on our recent work [10]

Polyakov loop fluctuations and Dirac mode on a lattice

Polyakov loop fluctuations

Operator formalism and Dirac mode on a lattice

Dirac spectrum representation of Polyakov loop fluctuations

Numerical analysis

Summary