PHYS-739 / 4 credits

Teacher(s): Guica Monica Maria, Mathys Grégoire Olivier, Papadodimas Kyriakos, Trevisani Emilio

Language: English

Remark: Next time: Fall


Every year


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. 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.


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


3. 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.


Invited lecturer: Monica Guica


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:

  • Understand the Conformal Bootstrap approach to Conformal Field Theory
  • Understand the AdS/CFT correspondence and its implications for Quantum Gravity
  • Apply Perform and explain calculations in CFT and Gravity

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

Indicidual project and oral exam.



Slava Rychkov, lectures notes on CFT,

David Simmos-Duffin, lecture notes on CFT,

Joao Penedones, lecture notes on AdS/CFT,

Moodle Link

In the programs

  • Exam form: Oral (session free)
  • Subject examined: Conformal Field theory and Gravity
  • Lecture: 28 Hour(s)
  • Exercises: 28 Hour(s)
  • Type: optional

Reference week

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