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Introduction to AdS/CFT
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
- Conformal field theories
- Non-abelian gauge-theories and large-N limit
- AdS spacetime
- The Holographic Correspondence
- Finite Temperature
- Confinement
- AdS/CFT from string theory
- (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
- M. Baggioli, A practical mini-course on applied holography, Lots of developed explicit calculations and tricks. Avaiable at https://arxiv.org/abs/1908.02667
- F. Benini, lectures given at SISSA. Avaiable at https://www.sissa.it/tpp/phdsection/descriptioncourse.php?ID=16
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.