# Coursebooks

## Conformal Field theory and Gravity

#### Lecturer(s) :

Augusto Penedones Fernandes João Miguel
Meineri Marco

English

Every year

#### Remarque

Every year / Next time: Fall 2018

#### Summary

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.

#### Content

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.

#### Keywords

gauge/gravity duality

conformal bootstrap

#### Learning Prerequisites

##### Required courses

Quantum Field Theory, General Relativity

##### Recommended courses

Gauge Theories and the Standard Model

#### Learning Outcomes

By the end of the course, the student must be able to:
• Formulate the bootstrap conditions on the CFT data.
• Use the gauge/gravity duality to describe QFT phenomena.
• Apply CFT methods to explain properties of continuous phase transitions.

#### Transversal skills

• Plan and carry out activities in a way which makes optimal use of available time and other resources.
• Continue to work through difficulties or initial failure to find optimal solutions.
• Make an oral presentation.
• Demonstrate the capacity for critical thinking
• Write a scientific or technical report.

#### 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.

#### Resources

##### Bibliography

Slava Rychkov, lectures notes on CFT, http://arxiv.org/abs/1601.05000

David Simmos-Duffin, lecture notes on CFT, http://arxiv.org/abs/1602.07982

Joao Penedones, lecture notes on AdS/CFT, https://arxiv.org/abs/1608.04948

### In the programs

• Semester
• Exam form
Multiple
• Credits
4
• Subject examined
Conformal Field theory and Gravity
• Number of places
30
• Lecture
28 Hour(s)
• Exercises
28 Hour(s)

### Reference week

Lecture
Exercise, TP
Project, other

### legend

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