Analytical formulae of the Polyakov and Wilson loops with Dirac eigenmodes in lattice QCD

Suganuma, Hideo; Doi, Takahiro; Iritani, Takumi

doi:10.1093/ptep/ptv184

Cited by 8 publications

(45 citation statements)

References 40 publications

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“…and find small contribution from low-lying physical-fermion modes ofK 4 to the Polyakov loop L P , because of the suppression factorλ 2l n ν in the sum.…”

Section: The Domain Wall (Dw) Fermionmentioning

confidence: 91%

“…To begin with, we study the Polyakov loop and Dirac modes in temporally odd-number lattice QCD [2][3][4], where the temporal lattice size N t (< N s ) is odd. In general, only gauge-invariant quantities such as closed loops and the Polyakov loop survive in QCD, according to the Elitzur theorem [6].…”

Section: Polyakov Loop and Dirac Modes In Temporally Odd-number Lattimentioning

confidence: 99%

“…(2), the functional trace of "non-closed line" is exactly zero [2][3][4] at each lattice gauge configuration.) In this way, we obtain the analytical relation between the Polyakov loop L P and the Dirac modes in QCD on the temporally odd-number lattice [2][3][4],…”

Section: Polyakov Loop and Dirac Modes In Temporally Odd-number Lattimentioning

confidence: 99%

“…(33), the extra degrees of freedom in the fifth dimension can be integrated out in the generating functional, and one obtains the four-dimensional physical-fermion kernelK 4 [17]. The physical fermion mode is given by the eigenmode |n ofK 4 , K 4 |n = iλ n |n ,λ n ∈ C.…”

Section: The Domain Wall (Dw) Fermionmentioning

confidence: 99%

“…In this paper, considering the essential role of low-lying Dirac modes to chiral symmetry breaking [6], we derive analytical relations between the Dirac modes and the confinement quantities, e.g., the Polyakov loop [2], its fluctuations [3] and the string tension [4], in the lattice QCD formalism.…”

Section: Introductionmentioning

confidence: 99%

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Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

et al. 2017

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Abstract. 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-toone correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass.

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“…and find small contribution from low-lying physical-fermion modes ofK 4 to the Polyakov loop L P , because of the suppression factorλ 2l n ν in the sum.…”

Section: The Domain Wall (Dw) Fermionmentioning

confidence: 91%

Section: Polyakov Loop and Dirac Modes In Temporally Odd-number Lattimentioning

confidence: 99%

Section: Polyakov Loop and Dirac Modes In Temporally Odd-number Lattimentioning

confidence: 99%

Section: The Domain Wall (Dw) Fermionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

et al. 2017

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Dirac-mode analysis for quark number density and its application for deconfinement transition

Doi

Kashiwa

2018

EPJ Web Conf.

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The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark mass regime. On the other hand, in the small quark mass region, the quark number density is investigated by using the quenched lattice QCD simulation. The quark number density is found to strongly depend on the low-lying Dirac modes while its sign does not change. This result leads to that the quark number holonomy is not sensitive to the low-lying Dirac modes. We discuss the confinement-deconfinement transition from the property of the quark number density and the quark number holonomy.

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Relating quark confinement and chiral symmetry breaking in QCD

Suganuma

Doi

Redlich

et al. 2017

J. Phys. G: Nucl. Part. Phys.

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Abstract. 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 λ n such as λ Nt−1 n , which behaves as a reduction factor for small λ 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.

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Analytical formulae of the Polyakov and Wilson loops with Dirac eigenmodes in lattice QCD

Cited by 8 publications

References 40 publications

Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

Dirac-mode analysis for quark number density and its application for deconfinement transition

Relating quark confinement and chiral symmetry breaking in QCD

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