Tom Hartman's Physics Homepage
Course Website: Quantum Gravity and Black Holes
These notes are a work in progress. They will usually contain more info than the actual lectures, including references. Please email me with any errors/corrections/comments/suggestions/etc!
- Note 1 - Gravity as an effective field theory -- Gravity in the IR, breakdown of the EFT, the Weinberg-Witten theorem, and some expectations for the UV.
- Note 2 - Laws of Black Hole Thermodynamics -- 1st and second laws of black hole thermodynamics
- Note 3 - Rindler space and intro to Hawking radiation -- Rindler space, near horizon metric of black holes, and a first look at periodicity in Euclidean time. (Lecture 3 did not quite follow the notes, I decided to present things in a different order -- so it contained parts of notes 3, 4 and 5.)
- Note 4 - path integrals in QFT -- 'Cutting' of path integrals; Preparation of states with Euclidean path integrals; Path integral representation of the ground state; Thermal partition function as path integral on cylinder
- Note 5 - Unruh and Hawking Radiation from the Path Integral -- Derivation of the Rindler density matrix; Importance of entanglement; purification and thermofield doubles; free-field example for Unurh radiation; information paradox.
- Note 6- The Gravitational Path Integral -- On-shell Euclidean action, free energy
- Note 7 - Thermodynamics of de Sitter - Temperature, action, entropy, and a path integral derivation of the gaussian fluctuations in the CMB.
- Note 8 - Hamiltonian and Symmetries of GR
- Note 9 - Symmetries of AdS3
- Note 10 - Preview of the AdS/CFT Correspondence
- Note 11 - Near horizon limits and Anti-de Sitter
- Note 12 - Scattering from the D1-D5-P Black String
- Note 13 - CFT Calculation of the black string absorption cross section -- Introduction to 2d CFT: complex coordinates, conformal transformations, primary fields, mapping the cylinder to the plane, and finite-temperature correlators; Calculation of absorption cross section in a thermal state.
- Note 14 - The statement of the AdS/CFT correspondence -- GKPW dictionary; requirements for a semiclassical gravity dual, large N and a spectral gap; strong/weak; the holographic principle; the example of IIB strings and N=4 Super-Yang-Mills.
- Note 15 - Correlation functions in AdS/CFT - The GKPW dictionary; Witten diagrams; large-N factorization.
- Note 16 - Black Hole Thermodynamics in AdS - Black hole phase and thermal AdS phase; Calculating the free energy; The Hawking-Page phase transition; Interpretation in CFT as deconfinement transition; Free energy at strong and weak coupling and the famous factor of 4/3.
- Note 17 - Eternal Black Holes and Entanglement - AdS black holes and the thermofield double formalism; Comments on the information paradox in AdS/CFT, and Maldacena's version of the information paradox for eternal black holes.
- Note 18 - Introduction to Entanglement Entropy - Definitions, scaling laws, and inequalities of entanglement entropy in quantum mechanics
- Note 19 - Entanglement in QFT - UV divergences, general structure, and consequences of Lorentz invariance
- Note 20 - Entanglement Entropy and the Renormalization Group - Measures of degrees of freedom; c-theorem, F-theorem, and a-theorem; entanglement methods of Casini and Huerta
- Note 21 - Holographic entanglement entropy - the Ryu-Takayanagi formula; example in 2d CFT; general comments
- Note 22 - Holographic entanglement at finite temperature - Ryu-Takayanagi applied to black holes
- Note 23 - The stress tensor in 2d CFT -- Ward identites, transformation laws, the central charge, Schwarzians, Casimir energy
- Note 24 - The stress tensor in 3d gravity -- Conformal transformations of AdS3; the Brown-Henneaux central charge
- Notes 25 and 26 - 2d CFT at finite temperature and black hole microstate counting -- The CFT partition function; CFT on a torus; Modular invariance; Cardy's entropy formula; and matching to the BTZ black hole.