Holography, probe branes and isoperimetric inequalities

Ferrari, Frank; Rovai, Antonin

doi:doi/10.1016/j.physletb.2015.06.004

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Holography, probe branes and isoperimetric inequalities

par Ferrari, Frank

;Rovai, Antonin

Référence Physics letters. Section B, 747, page (212-216)
Publication Publié, 2015-07

Article révisé par les pairs

Résumé :

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.

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