Quantum entropy of BMPV black holes and the topological M-theory conjecture

Abstract

We present a formula for the quantum entropy of supersymmetric five-dimensional spinning black holes in M-theory compactified on $C{Y}_3$, i.e., BMPV black holes. We use supersymmetric localization in the framework of off-shell five dimensional $N=2$ supergravity coupled to $I=1,\dots ,N_V+1$ off-shell vector multiplets. The theory is governed at two-derivative level by the symmetric tensor ${\mathcal{C}}_{IJK}$ (the intersection numbers of the Calabi-Yau) and at four-derivative level by the gauge-gravitational Chern-Simons coupling $c_I$ (the second Chern class of the Calabi-Yau). The quantum entropy is an $N_V+2$-dimensional integral parameterised by one real parameter ${\phi }^I$ for each vector multiplet and an additional parameter ${\phi }^0$ for the gravity multiplet. The integrand consists of an action governed completely by ${\mathcal{C}}_{IJK}$ and $c_I$, and a one-loop determinant. Consistency with the on-shell logarithmic corrections to the entropy, the symmetries of the very special geometry of the moduli space, and an assumption of analyticity constrains the one-loop determinant up to a scale-independent function $f({\phi }^0)$. For $f=1$ our result agrees completely with the topological M-theory conjecture of Dijkgraaf, Gukov, Nietzke, and Vafa for static black holes at two derivative level, and provides a natural extension to higher derivative corrections. For rotating BMPV black holes, our result differs from the DGNV conjecture at the level of the first quantum corrections.

References in corpus (51)

• Wilson loops in large N field theories
• Lecture Notes on Holographic Renormalization
• Supersymmetry and Attractors
• D--branes and Spinning Black Holes
• Black Hole Attractors and the Topological String
• Universality of Sypersymmetric Attractors
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Corrections to macroscopic supersymmetric black-hole entropy
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• New Connections Between 4D and 5D Black Holes
• Split States, Entropy Enigmas, Holes and Halos
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Lectures on Quantum Black Holes
• Nonperturbative black hole entropy and Kloosterman sums
• Quantum black holes, localization and the topological string
• Supersymmetric Index from Black Hole Entropy
• The BPS limit of rotating AdS black hole thermodynamics
• Chern-Simons terms and the Three Notions of Charge
• String Theory Effects on Five-Dimensional Black Hole Physics
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term
• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• All solutions of the localization equations for N=2 quantum black hole entropy
• Localization of the action in AdS/CFT
• Black Hole Hair Removal
• Precision Entropy of Spinning Black Holes
• All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Corrections to the statistical entropy of five dimensional black holes
• Black Hole Microstate Counting and its Macroscopic Counterpart
• The off-shell 4D/5D connection
• Near-horizon analysis of D=5 BPS black holes and rings
• Higher Derivative Corrections and Central Charges from Wrapped M5-branes
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• On the quantum entropy function in 4d gauged supergravity
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Gravitational Cardy Limit and AdS Black Hole Entropy
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• One-loop determinants for black holes in 4d gauged supergravity
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Curvature squared action in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet
• Dyonic black hole degeneracies in $\mathcal{N}=4$ string theory from Dabholkar-Harvey degeneracies
• Topological wave functions and the 4D-5D lift
• On the localization manifold of 5d supersymmetric spinning black holes

Cited by in corpus (4)

• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Localization on $Ad{S}_3\times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$