D ec 2 01 1 High temperature quark localization by Polyakov loops

We study the low eigenmodes of the overlap and staggered Dira c operator at high temperature. We show that the recently found localized quark modes obeyin g Poisson statistics are connected to physical gauge field objects with their size and density sc aling in the continuum limit. The localized modes are also strongly correlated with large fluc tuations of the Polyakov loop. Based on that we construct a random matrix model of the low Dirac mod es inspired by dimensional reduction. Our model reproduces the Poisson to random matri x transition seen in the lattice Dirac spectrum.