Fiches de cours 2018-2019


Conformal Field theory and Gravity


Lecturer(s) :

Augusto Penedones Fernandes João Miguel
Meineri Marco




Every year


Every year / Next time: Fall 2018


This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.


1. Scaling and Renormalization - quick review of phase transitions, critical exponents, block spin transformations, scaling variables and operators, renormalization group flows.

2. Conformal field theory - Conformal transformations, conformal algebra, local  operators (primaries and descendants), correlation functions, stress tensor, Weyl invariance, conformal Ward identities, Radial quantization (state-operator map), unitarity bounds, operator product expansion, conformal blocks (Casimir equation), conformal bootstrap, conformal anomaly, embedding space formalism, large N factorization.

3. Anti-de Sitter spacetime - Geometry, particle dynamics, free fields in AdS, interacting fields in AdS.

4. The AdS/CFT correspondence - quantum gravity as CFT, semi-classical limit and the large N expansion, the role of String Theory, black holes and thermodynamics, universal long range forces, entanglement entropy.


gauge/gravity duality

conformal bootstrap

Learning Prerequisites

Required courses

Quantum Field Theory, General Relativity

Recommended courses

Advanced Quantum Field Theory

Gauge Theories and the Standard Model

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Black board lectures and problem solving sessions.

Expected student activities

Attendance of lectures and problem solving sessions. Critical study of the material.


Assessment methods

Oral exam.

Small project including presentation and short written report.



Slava Rychkov, lectures notes on CFT,

David Simmos-Duffin, lecture notes on CFT,

Joao Penedones, lecture notes on AdS/CFT,

In the programs

    • Semester
    • Exam form
    • Credits
    • Subject examined
      Conformal Field theory and Gravity
    • Lecture
      28 Hour(s)
    • Exercises
      28 Hour(s)

Reference week

      Exercise, TP
      Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German