We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, Γ ∝ exp(Im[ p dr]), rather than, Γ ∝ exp(2Im[ p dr]), for the tunneling probability/decay rate one obtains twice the original Hawking temperature. The former expression for Γ is argued to be correct since p dr is invariant under canonical transformations, while p dr is not. Thus, either the tunneling methods of calculating Hawking radiation are suspect or the Hawking temperature is twice that originally calculated.

We discuss peculiarities of quantum fields in de Sitter space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Non-conformal quantum field theories in de Sitter space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-de-Sitter space: in de Sitter space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the quantum field theory under the de Sitter isometry and the (in)stability of de Sitter invariant states (and of dS space itself) under nonsymmetric perturbations.

The correspondence between the four-dimensional SU (N ), N = 4 SYM taken at large N and the type II B SUGRA on the AdS 5 ×S 5 background is considered. We argue that the classical equations of motion in the SUGRA picture can be interpreted as that of the renormalization group on the SYM side. In fact, when the D3-brane is slightly excited higher derivative terms in the field theory on its world-volume deform it form the conformal N = 4 SYM limit. We give arguments in favor of that the deformation goes in the way set by the SUGRA equations of motion. Concrete example of the s-wave dilaton is considered. Having in mind those facts, in this note we try to give a geometric interpretation of the renormalization group flow in the SYM theory. Our work is based on the proposed duality [10] between the four-dimensional large N SYM theory and type IIB SUGRA on a background which we describe below. Concretely, we argue that the classical equation of motion of the dilaton in the bulk SUGRA theory is nothing but the renormalization group equation for the SYM "coupling constant" on the D-brane world-volume [11]. As we discuss below, this fact is sensible if the dilaton -"coupling constant" -is excited and, hence, is a function of the four-dimensional coordinates. While if the dilaton is an arbitrary constant it remains to be the one at any energy scale. In the both cases the movement in the direction transversal to the D-brane is the renormalization group transformation [10,12] in the field theory on its world-volume.In fact, it is widely believed that super-strings suggest the regularization of field theory [13]. What is new in the D-brane case is that the regularization of their world-volume field theories can happen at much smaller energy scale than the Plank one, if some particular double scaling limit is taken [11,14,15]. The regularized theory should be considered as a vacuum in that of super-strings [10]. For after the regularization we are missing information 1