Equivariant localization in supergravity

Abstract

We show that supersymmetric supergravity solutions with an R-symmetry Killing vector are equipped with a set of equivariantly closed forms. Various physical observables may be expressed as integrals of these forms, and then evaluated using the Berline-Vergne-Atiyah-Bott fixed point theorem. We illustrate with a variety of holographic examples, including on-shell actions, black hole entropies, central charges, and scaling dimensions of operators. The resulting expressions depend only on topological data and the R-symmetry vector, and hence may be evaluated without solving the supergravity equations.

6 pages; very minor changes, published version

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• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Toric gravitational instantons in gauged supergravity
• NUTs, Bolts, and Spindles
• Branes wrapped on quadrilaterals
• On five-dimensional curvature squared supergravity and holography
• Holographic origin of $a$-maximization and higher-derivative AdS${}_5$/CFT${}_4$
• Bubbling saddles of the gravitational index
• Kodaira-Spencer Anomalies with Stora-Zumino Method