RANDOM-MATRIX THEORY AND SPECTRAL SUM-RULES FOR THE DIRAC OPERATOR INQCD

We construct a random matrix model that, in the large-N limit, reduces to the low-energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number o f flavors and any value of the QCD vacuum angle. In this model, moment s of the inverse squares of eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the valid ity. of the sum rules depends only on the symmetries of the theory but not on its details. To illustrate this point we show that the sum rul es hold for an interacting liquid of instantons. The physical interpre tations is that the way the thermodynamic limit of the spectral densit y near zero is approached is universal. However, its value, i.e. the c hiral condensate, is not.