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

Duality in N=1, D=10 Superspace and Supergravity with Tree Level Superstring Corrections

The equations of motion (e.m.'s) of the N=1, D=10 anomaly free supergravity, obtained in the framework of the superspace approach, are analyzed. The formal equivalence of the usual and dual supergravities is discussed at the level of e.m.'s. The great simplicity of the dual formulation is established. The possibillity of the lagrangian formulation of the dual supergravity is pointed out. The bosonic part of the lagrangian is constructed including anomaly compensating superstring corrections.Comment: It is the revised version where the spelling mistake in the Title is corrected. LaTeX, 11 pages, no figure