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Regular Seminar Leonid Shifrin (Brunel)
Chiral symmetry and its spontaneous breaking (ChSB ) play a major role in the low-energy dynamics of Quantum Chromodynamics (QCD). In the language of Dirac eigenvalues, ChSB imposes strong constraints on Dirac spectra, called Leutwyler-Smilga (LS) spectral sum rules. These sum rules were originally derived for QCD on rather general grounds. I will give an alternative simple combinatorial derivation of the LS sum rules for 1 flavor, based on cluster property and chiral decomposition. Further, I will sketch the exact microscopic (field theory) derivation of them in the closely related to QCD but much simpler 2-dimensional Schwinger model. I will also discuss several related topics including breaking of cluster property in multi-flavor QCD, Random Matrix Theory calculation of the leading mass dependence of the QCD partition function, and the so-called spectral duality.