Equivariant localization for D = 4 gauged supergravity
File(s)JHEP08(2025)211.pdf (1.11 MB)
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Author(s)
Genolini, Pietro Benetti
Gauntlett, Jerome P
Jiao, Yusheng
Lüscher, Alice
Sparks, James
Type
Journal Article
Abstract
We consider supersymmetric solutions of D = 4, N = 2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Such solutions admit an R-symmetry Killing vector, ξ, constructed as a bilinear in the Killing spinor. The Killing spinor bilinears can also be used to construct polyforms that are equivariantly closed under the action of the equivariant exterior derivative d<inf>ξ</inf> = d – ξ⌟. This allows one to compute various flux integrals and the on-shell action using localization, without solving any supergravity equations, just assuming the supersymmetric solutions exist. The flux integrals allow one to obtain important UV-IR relations, relating fixed point data in the bulk to data on the asymptotic AdS boundary, allowing one to express the gravitational free energy in terms of boundary SCFT data. We illustrate the formalism with a number of examples, including classes of solutions which are unlikely to be ever constructed in closed form.
Date Issued
2025-08-01
Date Acceptance
2025-07-16
Citation
The Journal of High Energy Physics, 2025, 2025 (8), pp.0-78
ISSN
1029-8479
Publisher
SpringerOpen
Start Page
0
End Page
78
Journal / Book Title
The Journal of High Energy Physics
Volume
2025
Issue
8
Copyright Statement
© The Authors. Article funded by SCOAP3 . 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
Publication Status
Published
Article Number
211
Date Publish Online
2025-08-26