On Four-Point Functions of Half-BPS Operators in General Dimensions

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte

Wireless propagation modeling by using ray-tracing

The asymptotic high frequency techniques, based on the Geometrical Optics (GO), the Geometrical Theory of Diffraction (GTD), and its extension such as the Uniform Theory of Diffraction (UTD), can be used to study the propagation of wireless electromagnetic signals in complex environments. Indeed, at high frequencies, it is possible to use the ray concept to trace the paths followed by electromagnetic waves from the transmitting to the receiving antenna, and to calculate the attenuation suffered by virtue of its interaction with the obstacles present in its environment. After a brief overview of the evaluation of electromagnetic fields by using the GO and/or the GTD/UTD, the fundamental geometric concepts of the ray-tracing algorithms are presented. Next, some acceleration techniques, necessary to efficiently model wireless propagation in outdoor and indoor environments, are discussed. Furthermore, leveraging the fact that the ray-tracing algorithm provides all the data necessary for a complete characterization of wireless propagation, it is used to derive some important parameters such as Path Loss, Delay Spread, channel frequency and impulse response, Power Delay Profile and Spreading Function