Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD

We compute the screening correlators in the sigma and eta' flavor singlet channels in finite temperature QCD with 2 light quark flavors. Together with the correlators in the pi and delta channels, these are used to discuss several issues related to symmetry restoration and the nature of the QCD phase transition. Our calculations span a range of temperature extending from approximately 125 MeV to 170 MeV and are carried out in the context of a staggered fermion formulation on a 16^3x8 lattice. In addition to the computation at a fixed quark mass (am_q=0.00625), we discuss the issue of the chiral limit. After careful consideration of the zero-mode shift lattice artefact, we present rather strong (topological) arguments in favor of the non-restoration of U_A(1) at T_c