We study an integral representation for the zeta function of the one-loop effective potential for a minimally coupled massive scalar field in D-dimensional de Sitter spacetime. By deforming the contour of integration we present it in a form suitable for letting the de Sitter radius tend to infinity, and we demonstrate explicitly for the case D=2 that the quantities ζ(0) and ζ(0) have the approp...

The non-linear nature of string theory on non-trivial backgrounds related to the AdS/CFT correspondence suggests to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit which describes point-like strings and the so called “near flat space” limit which connects two different sectors of string theory – pp-waves and “giant ma...

In no other living species does technology (or more precisely the need for technological development) play such an important role as it does in the human species. This rationale remains surely a matter of fact regarding the “traditional” or “common” condition of the man, understood as a being living “on the Earth” and with a specific and consolidated biological structure. However, any possible ...

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modi...

In the Penrose limit, AdS×S space turns into a Cahen-Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. I discuss how this algebra is mapped onto the holographic screen on the boundary of AdS. Furthermore, I show that the algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. By viewing the constraint...

Noncommutative multivariable versions of weighted shift operators arise naturally as ‘weighted’ left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these N tuples, and then find a family of inductive limit algebras determined by the periodic weighted shifts which can be regarded as noncommutative multivariable generalizations of the Bu...

We discuss the Penrose limit of pure AdS space, which is flat Minkowski space. Even though there is no holographic principle, we construct a " holographic screen " on which information on the corresponding CFT is encoded. The screen is obtained as a gauge-fixing condition upon restricting the Hilbert space to the states that are annihilated by the generator of scale transformations. This constr...

It is known that there exist two different classes of time dependent solutions in the form of space-like (or S)-branes in the low energy M/string theory. Accelerating cosmologies are known to arise from S-branes in one class, but not in the other where the time-like holography in the dS/CFT type correspondence may be more transparent. We show how the accelerating cosmologies arise from S-branes...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...