Fiches de cours 2017-2018

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Conformal Field theory and Gravity

PHYS-739

Lecturer(s) :

Augusto Penedones Fernandes João Miguel
Vacat .

Language:

English

Frequency

Every year

Remarque

Every year / Next time: Fall 2017

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. 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.

Keywords

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

Expected student activities

Understand the Conformal Bootstrap approach to Conformal Field Theory

Understand the AdS/CFT correspondence and its implications for Quantum Gravity

Perform and explain calculations in CFT and Gravity 

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