Holography, probe branes and isoperimetric inequalities
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Ferrari-2015-Holography, probe br.pdf
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Author(s)
Ferrari, Frank
Rovai, Antonin
Date Issued
June 2015
Journal
Physics Letters B
Publisher
Elsevier
Citation
Ferrari, Frank, and Antonin Rovai. “Holography, Probe Branes and Isoperimetric Inequalities.” Physics Letters B 747 (July 2015): 212–216.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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DOI of Published Version
https://doi.org/10.1016/j.physletb.2015.06.004
