Yuto NAKAJIMA

Faculty of Science, Kyoto University

Based on

YN and H. Suganuma, arXiv 2212.13874 [hep-th] (2022)

Quark-Hadron Seminar @YITP

May 26^th, 2023

Introduction�Quarks are liberated at high temperatures

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J. N. Guenther, Eur. Phys. J. A 57, 136 (2021)

A. M. Polyakov, Phys. Lett. B 72, 477 (1978);

L. Susskind, Phys. Rev. D 20, 2610 (1979)

Deconfinement

(QGP phase)

Confinement

(Hadron phase)

Introduction�Polyakov loops serve as order parameters

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Polyakov loops defined on lattice:

A. M. Polyakov, Phys. Lett. 59B, 82 (1975)

The thermal expectation value

(= partition function of a heavy quark) characterizes the confinement:

Link variable

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Deconfinement

(High temp.)

s.t.

Introduction �Deconfinement vacuum has center domains

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M. Asakawa et al., Phys. Rev. Lett. 110, 202301 (2013)

The Polyakov loop distribution has domain structure, separated from other domains by potential domain wall

Contents �Two main focuses of our recent work

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Contents �Two main focuses of our recent work

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R. B. Potts, Math. Proc. Cambridge Philos. 48,106 (1952)

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Partition function:

Hubbard-Stratonovich transformation

(Spatial-dependent) Landau functional

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Correlation function of the fluctuation:

After coarse graining, the action becomes continuous

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Correlation function of the fluctuation:

with

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Wilsonian action (without fermions)

・Strong coupling expansion (SCE)

・Integrate out the spatial link variables

: The product of Haar measures

J. Polonyi, Phys. Lett. B 110, 395 (1982);

F. Green and F. Karsch, Nucl. Phys. B 238, 297 (1984)

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F. Sannino, Phys. Rev. D 72 (2005)

Jacobian

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The fluctuation mass:

Contents�Two main focuses of our recent work

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②Evaluation of domain volume�To evaluate vacuum-to-vacuum transition

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Introduce time-dependence by hand

3d effective action for Polyakov loop phase

( )

②Evaluation of domain volume�To evaluate vacuum-to-vacuum transition

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②Evaluation of domain volume�Quantum correction violates no symmetry

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Consider a quantum correction to the effective potential

At one-loop order:

Can safely ignore the correction and tree level analysis is sufficient

②Evaluation of domain volume�Evaluate vacuum-to-vacuum transition rate

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Total transition rate

Thermal transition rate

Tunneling rate

(WKB approx.)

②Evaluation of domain volume�Evaluate vacuum-to-vacuum transition rate

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②Evaluation of domain volume�Vacuum lifetime can be calculated

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: The lifetime of stable vacuum domain

Unstable vacuum

Stable vacuum

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The lifetime increases rapidly at a specific volume

The “threshold” volume separates stable vacuum region and unstable vacuum region

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Future View�What if dynamical fermions exist?

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• The present work is at a quenched level

→The further analysis of the system including fermions

Phenomenological properties of domain walls

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• Improvement of various approximation

→Analysis without strong coupling expansion

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• Monte-Carlo lattice QCD simulation

→To demonstrate the QGP properties numerically