Analytical relation between confinement and chiral symmetry breaking in terms of Polyakov loop and Dirac eigenmodes in odd-number lattice 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 in QCD, i.e., \langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle, by considering {\rm Tr} (\hat{U}_4\hat{\not{D}}^{N_t-1}) on a temporally odd-number lattice, where the temporal lattice... Show more