LACES 2022

Lezioni Avanzate di Campi E Stringhe

Galileo Galilei Institute for Theoretical Physics, Arcetri  Italy
November, 28th - December, 16th

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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 4-7 can be rearranged in a different order and some of them possibly skipped. This will likely be decided as the course proceeds.


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 non-Wilsonian character of gravity

Black holes in AdS_d from Conformal field theory in d-1

(Non-AdS 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. Hawking-Page transition

The eternal black hole and the thermofield double

5. AdS/CFT from strings and D-branes

Gauge theory from open strings, gravity from closed strings

D-branes as gauge theories and as black holes

Decoupling limit and AdS/CFT

The D1D5 CFT

6. Low-dimensional 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 Ryu-Takayanagi formula

Holographic entanglement in vacuum and in thermal states

Entanglement wedges and bulk reconstruction


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; Einstein-Hilbert 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  
  First batch.  
Alice Bernamonti
Agnese Bissi
Davide Cassani
Carlo Maccaferri
Noppadol Mekareeya
Annalisa Anichini
Alessandra Gentili
Mauro Morandini
Mirella Ridi
Computer assistance:
Alessio Attardi
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