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LACES 2022 Lezioni Avanzate di Campi E Stringhe Galileo Galilei Institute for Theoretical Physics, Arcetri Italy


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Holography and Quantum Gravity Emparan Roberto  ICREA and University of Barcelona 

This is the outline of the course on "Holography and Quantum Gravity". Most of it is devoted to our currently best understood framework for quantum theories of gravity: the holographic AdS/CFT correspondence. There will be more detail on the gravitational side of the correspondence than on the field theory side. I don't expect to be able to appropriately cover all the topics below in these lectures (that is, without rushing a lot, which I intend not to do), but I'll try to provide lecture notes for all of them. I'll also give homework exercises as a complement to the lectures. The first three items are ground material that the rest of the lectures will build on, but from item 4 on, the course is modular: to a large extent, items 47 can be rearranged in a different order and some of them possibly skipped. This will likely be decided as the course proceeds. Syllabus 1. Motivation: The Black Hole Guide to the Quantum Theories of Gravity Quantum theory of General Relativity and its breakdown Transplanckian black hole dominance and the nonWilsonian character of gravity Black holes in AdS_d from Conformal field theory in d1 (NonAdS holography?) 2. The gravitational path integral Black hole thermodynamics: general aspects and Euclidean formalism The gravitational path integral Entropy and thermodynamics from gravitational action 3. Basics of AdS/CFT holography Geometry of AdS Fields in AdS / Operators in CFT Divergences and holographic renormalization The holographic stress tensor 4. Thermal states in AdS/CFT Phases of AdS black holes. HawkingPage transition The eternal black hole and the thermofield double 5. AdS/CFT from strings and Dbranes Gauge theory from open strings, gravity from closed strings Dbranes as gauge theories and as black holes Decoupling limit and AdS/CFT The D1D5 CFT 6. Lowdimensional models AdS3/CFT2. The BTZ black hole and its CFT dual AdS2, JT gravity and the Schwarzian action 7. Holography and entanglement Basics of entanglement Holographic entanglement entropy: the RyuTakayanagi formula Holographic entanglement in vacuum and in thermal states Entanglement wedges and bulk reconstruction Prerequisites It will be assumed the students have been exposed to: an intro course on GR; basics of the Schwarzschild solution, incl maximal analytic extension, and possibly its Penrose diagram; EinsteinHilbert action; the general notion that black holes satisfy thermodynamic laws, and that their horizon area corresponds to entropy. These NOTES contain other prerequisite background material that will be mentioned in the lectures but won't be covered in detail. Many students will already know well all this, but for others these notes may serve as remedial help or reminders. Most textbooks on GR cover well all the prerequisites, e.g. Sean Carroll's or Eric Poisson's books.  
Lecture notes  
1 Motivation  
2 Gravitational Path Integral  
3 Basics of AdS/CFT  
4 Thermal states in AdS/CFT  
5 Holography and entanglement  
6 Low dimensional models  
7 AdS/CFT from strings and branes  
Exercises  
First batch.  
Organisers: Alice Bernamonti Agnese Bissi Davide Cassani Carlo Maccaferri Noppadol Mekareeya 
Secretary: Annalisa Anichini Alessandra Gentili Mauro Morandini Housing: Mirella Ridi Computer assistance: Alessio Attardi 
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