Linking confinement to spectral properties of the Dirac operator

Abstract

We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.