Holography, probe branes and isoperimetric inequalities

In many instances of holographic correspondences between a d-dimensional boundary theory and a (. d+. 1)-dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean on-shell action of a (. d-. 1)-brane probing the bulk geometry and the Euclidean gravitational bulk action. This relation is crucial for the consistency of holography, yet it is non-trivial from the bulk perspective. In particular, we show that it relies on a nice isoperimetric inequality that must be satisfied in a large class of Poincaré-Einstein spaces. Remarkably, this inequality follows from theorems by Lee and Wang.

Anomalous transport in plasmas

The application of stochastic methods to the problem of particle and energy transport in turbulent plasmas is briefly reviewed. The "classical" Corrsin approximation is shown to be valid only in the limit of weak turbulence. The recently developed method of decorrelation trajectories is applicable over the whole range of turbulence intensities and yields the correct asymptotic behavior in the limit of very strong turbulence (subdiffusion). © 2004 Wiley Periodicals, Inc.