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# Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator

12/2011;

Source: arXiv

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**ABSTRACT:**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 of flavors and any value of the QCD vacuum angle. In this model, moments of the inverse squares of eigenvalues of the Dirac operator obey sum rules, which we conjecture to be universal. In other words, the validity 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 rules hold for an interacting liquid of instantons. The physical interpretations is that the way the thermodynamic limit of the spectral density near zero is approached is universal. However, its value, i.e. the chiral condensate, is not.Nuclear Physics A 01/1993; · 2.50 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limit provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator as recently discussed by Leutwyler and Smilga. Comment: 9 pages + 1 figure, SUNY-NTG-93/2Physical Review Letters 07/1993; 70(25):3852-3855. · 7.73 Impact Factor -
##### Article: Quark condensate in one-flavor QCD

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**ABSTRACT:**We compute the condensate in QCD with a single quark flavor using numerical simulations with the overlap formulation of lattice fermions. The condensate is extracted by fitting the distribution of low lying eigenvalues of the Dirac operator in sectors of fixed topological charge to the predictions of Random Matrix Theory. Our results are in excellent agreement with estimates from the orientifold large-N_c expansion. Comment: 12 pages, 4 figures, REVTeX4, v2: Small changes, extended introduction, published versionPhysical review D: Particles and fields 05/2006;

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