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Ferrari, Frank and Rovai, Antonin (2015): Holography, probe branes and isoperimetric inequalities. In: Physics Letters B, Vol. 747: pp. 212-216 [PDF, 295kB]


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 Poincare-Einstein spaces. Remarkably, this inequality follows from theorems by Lee and Wang.

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