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.

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.

Basics of QCD and Lattice QCD.- Relation Between Connement and Chiral Symmetry Breaking.- Generalization to Chiral Fermion on the Lattice.- Summary and Outlook.