Higher-Derivative Corrections and AdS${}_5$ Black Holes

Abstract

Using recent results in four-derivative 5d $\mathcal{N}=2$ minimal gauged supergravity, we evaluate the regularized on-shell action of the Euclidean solution in this theory that admits a Lorentzian continuation to an AdS${}_5$ black hole with one electric charge and two angular momenta. We focus on the supersymmetric limit of this solution and employ holography to show that the result can be expressed purely in terms of angular momentum fugacities and the 't Hooft anomalies for the $\mathrm{U}(1{)}_{\mathrm{R}}$ R-symmetry of the dual 4d $\mathcal{N}=1$ SCFT. This holographic calculation is in perfect agreement with recent studies of the 4d $\mathcal{N}=1$ superconformal index ``on the second sheet''. We illustrate the utility of these results in two classes of 4d $\mathcal{N}=1$ holographic SCFTs that have 't Hooft anomalies with suitable large $N$ behavior that leads to non-trivial corrections at first subleading order in the $1/N$ expansion. We also explicitly calculate the Wald entropy of the black hole solution and delineate the leading four-derivative corrections to the Bekenstein-Hawking entropy.

7 pages, higher-derivative computations done with the Mathematica package available at https://github.com/waskou/SolutionsX; v2: corrections and comments added concerning the entropy formula, ancillary files available at https://github.com/waskou/SolutionsX

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• On curvature-squared invariants of minimal five-dimensional supergravity from superspace
• Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity
• Improved Reall-Santos method for AdS black holes in general 4-derivative gravities
• The extremal Kerr entropy in higher-derivative gravities
• Consistent truncations in higher derivative supergravity
• Higher derivative corrections to Kerr-AdS black hole thermodynamics
• Background subtraction method is not only much simpler, but also as applicable as covariant counterterm method
• Bulk-Boundary Thermodynamics of Charged Black Holes in Higher Derivative Theory
• Wrapped M5-branes and AdS${}_5$ Black Holes
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• On five-dimensional curvature squared supergravity and holography
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• Holographic origin of $a$-maximization and higher-derivative AdS${}_5$/CFT${}_4$