Analytical Relation between Quark Confinement and Chiral Symmetry Breaking in QCD

We study the relation between quark confinement and spontaneous chiral-symmetry breaking directly in QCD. In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop \langle L_P \rangle and the Dirac eigenvalues \lambda_n, i.e., \langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle, on a... Show more