Localization of the free energy in supergravity

Abstract

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to vector multiplet matter. This allows one to compute the free energy without solving any supergravity equations, just assuming the solutions exist. As well as recovering some known results in the literature with ease, we also present new supergravity results that match with holographically dual field theory computations.

6 pages; v3: corrected typos

References in corpus (25)

• AdS/CFT Correspondence and Symmetry Breaking
• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• G-Structures and Wrapped NS5-Branes
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Accelerating Black Holes and Spinning Spindles
• Black Hole Thermodynamics with Conical Defects
• Thermodynamics of accelerating and supersymmetric $Ad{S}_4$ black holes
• Gluing gravitational blocks for AdS black holes
• The Scalar Chemical Potential in Cosmological Collider Physics
• The supersymmetric NUTs and bolts of holography
• Localization of the action in AdS/CFT
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Rotating attractors and BPS black holes in $Ad{S}_4$
• Multi-charge accelerating black holes and spinning spindles
• Equivariant localization in supergravity
• Matter-coupled supersymmetric Kerr-Newman-AdS${}_4$ black holes
• Scattering equations, generating functions and all massless five point tree amplitudes
• Super Yang-Mills, division algebras and triality
• Localization and Attraction
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• Localizing Wrapped M5-branes and Gravitational Blocks
• Stability of generalized Einstein-Maxwell-scalar black holes

Cited by in corpus (3)

• Toric gravitational instantons in gauged supergravity
• NUTs, Bolts, and Spindles
• Bubbling saddles of the gravitational index