Journal of High Energy Physics

, 2019:252 | Cite as

Localization of the action in AdS/CFT

  • Pietro Benetti GenoliniEmail author
  • Juan Manuel Perez Ipiña
  • James Sparks
Open Access
Regular Article - Theoretical Physics


We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS4/CFT3 correspondence. Such solutions are equipped with a supersymmetric Killing vector, and we show that the holographically renormalized action may be expressed entirely in terms of the weights of this vector field at its fixed points, together with certain topological data. In this sense, the classical gravitational partition function localizes in the bulk. We illustrate our general formula with a number of explicit examples, in which exact dual field theory computations are also available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes, as well as black hole solutions. Our simple topological formula also allows us to write down the action of any solution, provided it exists.


AdS-CFT Correspondence Supergravity Models Black Holes in String Theory Supersymmetric Gauge Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.

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