Introduction to AdS/CFT

Diploma(s)
Place
ENS-PSL
Spring semester
Level Master 2 3 ECTS - English
Instructor(s) Francesco NITTI ( Université de Paris Cité )
Education office

This is an introductory course presenting the basics of the AdS/CFT duality. On the way, it will present some interesting physical concepts which are worth being acquainted wth,  independently of anti-de Sitter or string theory, such as for example aspects of: confromal filed theories in d>2, the renormalization group, non-abelian gauge theories,  the large-N limit, black hole thermodynamics, semiclassical gravity. 

 

Syllabus

Planning

  1. Conformal field theories
  2. Non-abelian gauge-theories and large-N limit
  3. AdS spacetime 
  4. The Holographic Correspondence
  5. Finite Temperature 
  6. Confinement 
  7. AdS/CFT from  string theory 
  8. (Holographic RG flows)

References

These are the three main references that I suggest:

  • H. Nastase, Introduction to the ADS/CFT Correspondence, Cambridge University Press 2015.

This is a dedicated textbook, which starts from the very basics and explains the basis of GR, QFT, string theory and everything else needed as a background (although some of the background material is stripped down to the essential). (it may not be easy to find though)

  • A. Zaffaroni, Introduction to the AdS/CFT correspondence, Lecture notes for various courses given around 2010. 

Easy to follow, does not use string theory until half-way through the course, and when it does it makes the effort of explaining the basic ingredients.  Available at: http://virgilio.mib.infn.it/~zaffaron/lectures.html

 

  • J. Penedones, Tasi Lectures on AdS/CFT

Again no strings required. CFT part very well developed. Available at: https://arxiv.org/abs/1608.04948

 

There are plenty of other reviews and lecture notes on AdS/CFT.  A few of them are:

  • MAGOO

 The classic review paper on the subject, written  by the founding fathers. Not easy but  contains a thorough discussion of stringy stuff, susy and calculations of the first checks of the correspondence.  Available at:

https://arxiv.org/abs/hep-th/9905111

 

 

For background material on QFT, gauge theories and General Relativity, in case you want a crash course or a review, I suggest the excellent lectures by David Tong on both subjects, which can be found here: http://www.damtp.cam.ac.uk/user/tong/teaching.html

Prerequisites

Good knowledge of (perturbative) QFT and General Relativity.

No previous knoweledge  of string theory is required. 

Following the ICFP  String Theory course together with Intro to AdS/CFT is  suggested, but not necessary. 

Evaluation

There will be a written exam at the end.