Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop

We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched $SU(3)$ gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and get their main contribution from the IR end of the spectrum. They are approximately proportional to the Polyakov loop. In contrast to earlier studied spectral sums, some of them are expected to have a well-defined continuum limit.