Lectures on AdS Black Holes, Holography and Localization

Abstract

In these lectures I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimensions equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS${}_4$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS${}_5$ black holes.

83 pages, 2 figures; based on lectures given at CERN Winter School 2017 and ICTP School on Supersymmetric Localization, Holography and Related Topics 2018. v3: version to appear on Living Reviews in Relativity

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Supersymmetric multi-charge AdS_5 black holes
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Witten Index and Wall Crossing
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Localization on Hopf surfaces
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Brane Tilings and M2 Branes
• Supersymmetric Index from Black Hole Entropy
• Arithmetic of Quantum Entropy Function
• The asymptotic growth of states of the 4d N=1 superconformal index
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• The BPS limit of rotating AdS black hole thermodynamics
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Universal RG Flows Across Dimensions and Holography
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Bethe/Gauge correspondence on curved spaces
• Gluing gravitational blocks for AdS black holes
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Supersymmetric phases of 4d N=4 SYM at large N
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• AdS black holes and finite N indices
• Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes
• Static BPS Black Holes in AdS4 with General Dyonic Charges
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Rotating Black Hole Entropy from M5-branes
• Universal 3d Cardy Block and Black Hole Entropy
• 1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space
• Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Comments on the Casimir energy in supersymmetric field theories
• Black hole entropy function for toric theories via Bethe Ansatz
• Equal charge black holes and seven dimensional gauged supergravity
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• Anomalies, Black strings and the charged Cardy formula
• Matter-coupled supersymmetric Kerr-Newman-AdS${}_4$ black holes
• Toric geometry and the dual of $c$-extremization
• Static BPS black holes in U(1) gauged supergravity
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Twisting with a Flip (the Art of Pestunization)
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• Thermodynamics at the BPS bound for Black Holes in AdS
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• Black hole microstate counting in Type IIB from 5d SCFTs
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Microstates of rotating AdS${}_5$ strings
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• One-loop determinants for black holes in 4d gauged supergravity
• Dimensional reduction of BPS attractors in AdS gauged supergravities
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Probing the EVH limit of supersymmetric AdS black holes
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Rotating black holes in the FI-gauged $N=2$, $D=4$ ${\overline{\mathbb{C}\text{P}}}^n$ model
• More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3
• Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds

Cited by in corpus (55)

• The BPS limit of rotating AdS black hole thermodynamics
• Supersymmetric phases of 4d N=4 SYM at large N
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Corrections to AdS${}_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Universal 3d Cardy Block and Black Hole Entropy
• Rotating Black Hole Entropy from M5-branes
• Supersymmetric solitons and a degeneracy of solutions in AdS/CFT
• Delayed Deconfinement and the Hawking-Page Transition
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• Black hole entropy function for toric theories via Bethe Ansatz
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• Information transfer with a twist
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Gravitational Cardy Limit and AdS Black Hole Entropy
• Stringy corrections to the entropy of electrically charged supersymmetric black holes with ${\mathrm{AdS}}_5\times S^5$ asymptotics
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Boundary terms and conserved charges in higher-derivative gauged supergravity
• Non-topological logarithmic corrections in minimal gauged supergravity
• Non-perturbative correction on the black hole geometry
• The dark (BPS) side of thermodynamics in Minkowski${}_4$
• Black Hole Entropy from Quantum Mechanics
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• The 5d Superconformal Index at Large $N$ and Black Holes
• New phases of $\mathcal{N}=4$ SYM at finite chemical potential
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Microscopic Entropy of AdS${}_3$ Black Holes Revisited
• Magnetic charge and black hole supersymmetric quantum statistical relation
• Uniqueness of supersymmetric AdS${}_5$ black holes with $SU(2)$ symmetry
• The extremal Kerr entropy in higher-derivative gravities
• The Phase Diagram of BPS Black Holes in AdS${}_5$
• On the uniqueness of supersymmetric AdS${}_5$ black holes with toric symmetry
• Unitary matrix models and random partitions: Universality and multi-criticality
• Exact holographic RG flows in extended SUGRA
• The $\mathcal{N}=2$ Prepotential and the Sphere Free Energy
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• How to Build a Black Hole out of Instantons
• Black Hole Entropy, Quantum Corrections and EFT Transitions
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• Supersymmetric asymptotically locally AdS${}_5$ gravitational solitons
• Gravitational Blocks: Symplectic Covariance Unveiled
• Thermodynamics of Near BPS Black Holes in AdS${}_4$ and AdS${}_7$
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Thermodynamics of BPS and Near-BPS AdS6 Black Holes
• Lumos Extrema
• All separable supersymmetric AdS${}_5$ black holes
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Wrapped M5-branes and AdS${}_5$ Black Holes
• The Holographic Contributions to the Sphere Free Energy
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Off-shell phase diagram of BPS black holes in AdS${}_5$