Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass

Dirac spectrum representation of Polyakov loop fluctuations in lattice QCD

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 semianalytically 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.Comment: 7 pages and 1 figure. Proceeding of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japan. Also regarded as the Proceeding of the 4th International Conference on new Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Conference Center of the Orthodox Academy of Crete, Crete, Greec

Relating Quark Confinement and Chiral Symmetry Breaking in QCD

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $\lambda_n$ such as $\lambda_n^{N_t-1}$, which behaves as a reduction factor for small $\lambda_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities,while they are essential for chiral symmetry breaking. These relations indicate no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively, and find the similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.Comment: 20 pages, 10 figures. arXiv admin note: text overlap with arXiv:1611.0874

Christopher Simpson The Division-Viol, or, The Art of PLAYING Extempore upon a GROUND. EDITIO SECVNDA Dedication & Recommendation

本訳稿はChristopher Simpson (1605頃－1669) 著 The Division-Viol, or, The Art of PLAYING Ex tempore upon a GROUND. DIVIDED INTO THREE PARTS. EDITIO SECVNDA, London, 1665 の著者による献辞および楽譜出版権所有者による推薦文の全訳である