Conformal Field theory and Gravity
PHYS-739 / 4 credits
Teacher(s): Guica Monica Maria, Mathys Grégoire Olivier, Papadodimas Kyriakos, Trevisani Emilio
Language: English
Remark: Next time: Fall
Frequency
Every year
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.
Note
Invited lecturer: Monica Guica
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
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.
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
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)