[en] It is well known that at the temperature different from the Hawking temperature there appears a conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such metrics. It allows to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions. It corresponds to the results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison to the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized with the renormalization of the gravitational coupling. (author). 35 refs

[en] The string model in terms of the two-dimensional differential forms of arbitrary rank is formulated. The local supersymmetric string action with local conformal and Lorentz symmetries is constructed. The connection with topological quantum field theory is discussed. Covariant quantization of the model is investigated. The critical space-time dimension is found to be d=4. (author). 14 refs

[en] We describe the physical situation in which the consideration of the fermionic vacuum bundle over gauge group manifold is useful. The bundle curvature turns out to be connected with the commutator gauge anomaly. This allows to consider the problem where this curvature is manifested. (author). 17 refs

[en] The 2 D gravity described by the action which is as arbitrary function of the scalar curvature f(R) is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function f R1nR the model coupled with scalar (conformal) matter is exactly integrated and is shown to describe a black hole of the 2 D dilaton gravity type. The influence of one-loop quantum corrections on a classical black hole configuration is studied by including the Liouville-Polyakov term. The resulting model turns out to be exactly solvable. The general solution is analyzed and shown to be free from the space-time singularities for a certain number of scalar fields. 21 refs., 5 figs

[en] A new superstring model using antisymmetric tensor fields is suggested. It is shown that critical dimension of the model appears arbitrary: D=4N, N=1, 2, etc

[en] The 2 D model of gravity with dyad e^a and the Lorentz connection one-form ω as independent gravitational variables coupled with rd massless Dirac matter is considered. It is shown that the classical equations of motion are exactly integrated. 12 refs. (author)

[en] We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4 D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at r=0 is shifted to the finite radius r_min ∼ r_PL, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius. (author). 17 refs.; 4 figs

[en] The spinor theory within the framework of inhomogeneous differential forms formalism is discussed. The possibility of the description of fermions by means of Ivanenko-Landau-Keler equation and its relation to the standard Dirac equation is considered

[en] One-loop divergences appearing in the entropy of a quantum black hole are proven to be completely eliminated by the standard renormalization of both the gravitational constant and other coefficients by the R²-terms in the effective gravitational action. The essential point of the proof is that due to the higher order curvature terms the entropy differs from the Bekenstein-Hawking one in the Einstein gravity by the contributions depending on the internal and external geometry of the horizon surface. 15 refs

[en] We describe the anomaly of the Virasoro algebra as the curvature in some bundle over the loop space. (orig.)