Analytical Formulae linking Quark Confinement and Chiral Symmetry Breaking*
1 Department of Physics, Kyoto University, Kyoto 606-8502, Japan
2 Institute of Theoretical Physics, University of Wroclaw, PL-50204 Wroclaw, Poland
3 Extreme Matter Institute EMMI, GSI, Planckstr. 1, D-64291 Darmstadt, Germany
4 Department of Physics, Duke University, Durham, North Carolina 27708, USA
5 Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main, Germany
a e-mail: email@example.com
Published online: 4 November 2016
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.
© The Authors, published by EDP Sciences, 2016
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