Lectures on Quantum Black Holes

Abstract

In these notes we describe recent progress in understanding finite size corrections to the black hole entropy. Much of the earlier work concerning quantum black holes has been in the limit of large charges when the area of the even horizon is also large. In recent years there has been substantial progress in understanding the entropy of supersymmetric black holes within string theory going well beyond the large charge limit. It has now become possible to begin exploring finite size effects in perturbation theory in inverse size and even nonperturbatively, with highly nontrivial agreements between thermodynamics and statistical mechanics. Unlike the leading Bekenstein-Hawking entropy which follows from the two-derivative Einstein-Hilbert action, these finite size corrections depend sensitively on the phase under consideration and contain a wealth of information about the details of compactification as well as the spectrum of nonperturbative states in the theory. Finite-size corrections are therefore very interesting as a valuable window into the microscopic degrees of freedom of the quantum theory.

79 pages, based on lectures given at the summer school 'Strings and Fundamental. Physics 2010' in Munich

References in corpus (11)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Comments on the Spectrum of CHL Dyons
• Entropy Function and AdS(2)/CFT(1) Correspondence
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Re-Recounting Dyons in N=4 String Theory
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Genus Two Surface and Quarter BPS Dyons: The Contour Prescription

Cited by in corpus (16)

• The AdS/CFT Correspondence
• Behavior of Quasinormal Modes and high dimension RN-AdS Black Hole phase transition
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Dynamics for a 2-vertex Quantum Gravity Model
• Evidence for galaxy dynamics tracing background cosmology below the de Sitter scale of acceleration
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• Black Holes with Intrinsic Spin
• Black Holes as Conformal Field Theories on Horizons
• Two critical phenomena in the exactly soluble quantized Schwarzschild black hole
• Non-extremal black hole solutions from the c-map
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• Extremal Black Hole Entropy from Horizon Conformal Field Theories
• Quasimodular forms and sl(m|m)^ characters
• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
• Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry
• A Scenario for Strong Gravity in Particle Physics: An alternative mechanism for black holes to appear at accelerator experiments