Equivariant localization for AdS/CFT
File(s)
Published version
Author(s)
Genolini, Pietro Benetti
Gauntlett, Jerome P
Sparks, James
Type
Journal Article
Abstract
We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS5 × M6 and AdS3 × M8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed.
Date Issued
2024-02-01
Date Acceptance
2023-01-09
Citation
The Journal of High Energy Physics, 2024, 2024 (2)
ISSN
1029-8479
Publisher
SpringerOpen
Journal / Book Title
The Journal of High Energy Physics
Volume
2024
Issue
2
Copyright Statement
© The Authors. 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.
License URL
Identifier
http://dx.doi.org/10.1007/jhep02(2024)015
Publication Status
Published
Article Number
15
Date Publish Online
2024-02-01