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It is known that contrary to expectations, the order parameter of chiralsymmetry breaking, the Dirac spectral density at zero virtuality does notvanish above the critical temperature of QCD. Instead, the spectral densitydevelops a pronounced peak at zero. We show that the spectral density in thepeak has large violations of the expected volume scaling. This anomalousscaling and the statistics of these eigenmodes is consistent with them beingproduced by mixing instanton and antiinstanton zero modes. Consequently, weshow that a nonvanishing topological usceptibility implies a finite density ofeigenvalues around zero, which can have implications on the restoration ofchiral symmetry above the critical temperature.

Topology and the Dirac Spectrum in Hot QCD