Based on the extended BRST formalism of Batalin, Fradkin and Vilkovisky, we perform a general algebraic analysis of the BRST anomalies in superstring theory of Neveu-Schwarz-Ramond. Consistency conditions on the BRST anomalies are completely solved. The genuine super-Virasoro anomaly is identified with the essentially unique solution to the consistency condition without any reference to a parti...

A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Si...

Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Λ. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either vanish, or are constants depending on Λ. Even all higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are shown to be trivial if a t...

In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for Higgs inflationary model recently introduced framework geometrical scalar–tensor theory gravity. scenario inflaton field has its origin Weyl background geometry. We found nearly scale invariance power spectrum linear metric. For certain parameters obtain values spectral index ns a...

TIn this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For manifolds, pseudosymmetric cases investigated some interesting results obtained. We show that semisymmetric is of constant sectional curvature. also obtain an $\eta$-Einstein manifold. Finally, we support our topic with example.

Asymptotic equalities are obtained for the least upper bounds of approximations functions from classes W?,?r by generalized Abel-Poisson integrals P?(?),0<??2, case r>? in uniform metric, which provide solution to Kolmogorov–Nikol’skii problem given method approximation on Weyl-Nagy classes.

In 1939 Weyl showed that the volume of spherical tubes around compact submanifolds M Euclidean space depends solely on induced Riemannian metric M. Can this intrinsic nature tube be preserved for with more general cross sections D than round ball? Under sufficiently strong symmetry conditions answer turns out to yes.

In this paper, we study closed four-dimensional manifolds. particular, show that under various new pinching curvature conditions (for example, the sectional is no more than 5/6 of smallest Ricci eigenvalue) then manifold definite. If restricting to a metric with harmonic Weyl tensor, it must be self-dual or anti-self-dual same conditions. Similarly, if an Einstein metric, either complex project...

Let X : (S, g) → R be a C isometric embedding of a C 4 metric g of non-negative sectional curvature on S into the Euclidean space R. We prove a priori bounds for the trace of the second fundamental form H , in terms of the scalar curvature R of g, and the diameter d of the space (S, g). These estimates give a bound on the extrinsic geometry in terms of intrinsic quantities. They generalize esti...

The equations of General Relativity are recast in the form a wave equation for Weyl tensor. This allows to reformulate gravitational theory terms curvature waves, rather than metric waves. existence two transverse polarization states waves is proven and linearized approximation quadrupole formula rederived. A perturbative scheme extend result non-linear regime outlined.