Localization of the action in AdS/CFT

• Published in: The journal of high energy physics Vol. 2019; no. 10; pp. 1 - 45
• Main Authors: Genolini, Pietro Benetti, Ipiña, Juan Manuel Perez, Sparks, James
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes in String Theory; Classical and Quantum Gravitation; Elementary Particles; Field theory; Fields (mathematics); High energy physics; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supergravity; Supergravity Models; Supersymmetric Gauge Theory; Supersymmetry; Topology; Black Holes in String Theory; AdS-CFT Correspondence; Supergravity Models; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2019)252

A bstract We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS 4 /CFT 3 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.