Dirac operator spectral density and low energy sum rules

The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral density, obtained from the partially quenched chiral perturbation theory is shown to be compatible with low energy sum rules, obtained earlier.Comment: 8 pages, latex, published version; NLO QCD correction to the Dirac operator spectral density is added to the tex

Fivebrane Lagrangian with Loop Corrections in Field-Theory Limit

Equations of motion and the lagrangian are derived explicitely for Dual D=10, N=1 Supergravity considered as a field theory limit of a Fivebrane. It is used the mass-shell solution of Heterotic String Bianchi Identites obtained in the 2-dimensional $\sigma$-model two-loop approximation and in the tree-level Heterotic String approximation. As a result the Dual Supergravity lagrangian is derived in the one-loop Five-Brane approximation and in the lowest 6-dimensional $\sigma$-model approximaton.Comment: 21 page

Chiral Condensates, Q_7 and Q_8 Matrix Elements and Large-N_c QCD

The correlation function of a $V-A$ current with a $V+A$ current is discussed within the framework of QCD in the limit of a large number of colours $N_c$. Applications to the evaluation of chiral condensates of dimension six and higher, as well as to the matrix elements of the $Q_7$ and $Q_8$ electroweak penguin operators are discussed. A critical comparison with previous determinations of the same parameters has also been made.Comment: Layout modified, size of first figure correcte