Introduction to AdS/CFT

Question

AdS/CFT seems like a really hot topic and I'd like to start reading about. I am looking for the best introduction at my level, i.e. I have a background in QFT, CFT and general relativity at the level of a master student in theoretical physics. What would you recommend me to start tackling the subject? I have been looking for resources and so far I have noticed:

• these synthetic introductory lectures by Horatiu Nastase

• the videos of lectures done by P. Vieira at Perimeter for Perimeter Scholar International students:

• the subject starts entering the most recent textbooks on string theory. We have the Schwartz and Becker and also the Kiritsis

I probably missed a lot of resources, as the literature on the subject is already quite huge. I would really appreciate some advice on that, as I already had the frustration of losing my time on not-so-good books when started to learn something new, so if I could (to the best) avoid that this time...

Answer 1

As of 2015, there is a brand new book that's dedicated solely to gauge/gravity duality. The book is fittingly called Gauge/Gravity Duality, and it was written by Erdmenger & Ammon, based on a course that Erdmenger has been teaching over the past years at LMU Munich (although the book contains much more than be covered in a single course). Lecture notes for (an older iteration of) the course can be found here (link dead now, available through the Wayback Machine).

After about 175 pages of introduction to the necessary prerequisites, the book devotes ~200 pages to AdS/CFT, after which further applications of gauge/gravity duality are treated in the final 150 or so pages.

On the site for the course Erdmenger teaches at LMU (link may expire), Erdmenger suggests the following papers to her students as supplementary reading:

• O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183, arXiv:hep-th/9905111.

• E. D'Hoker and D. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, arXiv:hep-th/0201253.

• J. Petersen, Introduction to the Maldacena conjecture on AdS/CFT, Int. J. Mod. Phys. A 14 (1999) 3597, arXiv:hep-th/9902131.

• J. Erdmenger, Introduction to Gauge/Gravity Duality, Lect.Notes Phys. 851 (2012) 99-145.

• D. Son and A. Starinets, Viscosity, Black Holes, and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95, arXiv:0704.0240 [hep-th].

• J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81 arXiv:0711.4467 [hep-th].

• J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518.

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Other suggestions from previous (now-deleted) answers:

Lecture notes from Raman Sundrum: "Fixed Points to the Fifth Dimension"

Answer 2

1. Introduction to the AdS/CFT Correspondence by Horațiu Năstase (this book is a highly updated version of the notes that OP mentioned)
2. Gauge/Gravity Duality: Foundations and Applications by Johanna Karen Erdmenger and Martin Ammon
3. AdS/CFT Duality User Guide by Makoto Natsuume

The above 3 books are good introductions. Năstase covers more topics and is more pedagogical than Erdmenger and Ammon. Erdmenger and Ammon is more advanced than Năstase. Natsuume covers the least number of topics and is the easiest to read. All 3 cover the prerequisites before going into the AdS/CFT Correspondence. You can read this book review that compares the above 3 books.

Other books:

4. AdS/CFT Correspondence in Condensed Matter by Antonio Sergio Teixeira Pires
5. String Theory Methods for Condensed Matter Physics by Horațiu Năstase

These 2 are for Condensed Matter Physicists.

6. Holographic Entanglement Entropy by Mukund Rangamani and Tadashi Takayanagi

This book is mainly related to the topics of AdS/CFT related to the Ryu–Takayanagi conjecture.

Very short reviews:

7. TASI 2003 Lectures on AdS/CFT Juan M. Maldacena https://arxiv.org/abs/hep-th/0309246
8. TASI lectures on AdS/CFT Joao Penedones https://arxiv.org/abs/1608.04948
9. TASI Lectures on the Emergence of the Bulk in AdS/CFT Daniel Harlow https://arxiv.org/abs/1802.01040