Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking

1. Front Matter

   Pages i-xii

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2. Basics of QCD and Lattice QCD

   • Takahiro Doi

   Pages 1-12

3. Relation Between Confinement and Chiral Symmetry Breaking

   • Takahiro Doi

   Pages 13-46

4. Generalization to Chiral Fermion on the Lattice

   • Takahiro Doi

   Pages 47-55

5. Summary and Outlook

   • Takahiro Doi

   Pages 57-59

This thesis focuses on an unresolved problem in particle and nuclear physics: the relation between two important non-perturbative phenomena in quantum chromodynamics (QCD) – quark confinement and chiral symmetry breaking. The author develops a new analysis method in the lattice QCD, and derives a number of analytical formulae to express the order parameters for quark confinement, such as the Polyakov loop, its fluctuations, and the Wilson loop in terms of the Dirac eigenmodes closely related to chiral symmetry breaking. Based on the analytical formulae, the author analytically as well as numerically shows that at finite temperatures there is no direct one-to-one correspondence between them. The thesis describes this extraordinary achievement using the first-principle analysis, and proposes a possible new phase in which quarks are confined and chiral symmetry is restored.

• Lattice QCD
• Quark Confinement
• Chiral Symmetery Breaking
• Dirac Eigenmode
• Elitzur's Theorem
• Banks-Casher Relation
• Polyakov Loop
• Wilson Loop
• Overlap-fermion
• Kogut-Susskind Formalism

• Nishina Center, RIKEN, Saitama, Japan

  Takahiro Doi

Dr. Takahiro Doi is a special postdoctral researcher (SPDR) at RIKEN. His work is concerned with the theory of particle and nuclear physics. He received his Bachelor, Master and Ph.D. from the Department of Physics, Kyoto University in 2012, 2014 and 2017, respectively. He was awarded a research fellowship for young scientists for 2015 to 2017 by the Japan Society for Promotion of Science (JSPS), and his research was supported by the JSPS.

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