What is the recommended resource for learning the basics of AdS/CFT?

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In summary, you should read Natsuume's "AdS/CFT Duality User Guide" if you want to learn about AdS/CFT.
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I'm looking to start learning the basics of AdS/CFT, in particular AdS/CFT integrability, over the summer before I start grad school. By the time I finish my undergrad I will have a good background in QFT (first 12 chapters of Peskin & Schroeder), GR (Sean Carroll's notes and Wald), quantum integrability (doing a research project in this area) as well as various pure maths subjects (relevant ones probably being algebraic topology, functional analysis and representation theory). I know a little CFT already but not much. I don't know any Super Yang Mills yet either.

I'm looking for everything I need to get acquainted with AdS/CFT. I've looked at the review papers by Beisert et al but the non-integrability stuff is a bit over my head. I'm guessing Strings are necessary. Please list any books, review papers etc I should look at. Thanks!
 
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This one is quite easy to read, but has not so much about integrability.

http://arxiv.org/abs/0909.0518
Holographic duality with a view toward many-body physics
John McGreevy
 
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I like that one. It has a lot of intuitive reasoning.
 
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I've tried many introductions to AdS/CFT, including the ones mentioned above, but until recently neither of them really worked for me. They all created more confusion than understanding to me.

But a few days ago I discovered Natsuume's "AdS/CFT Duality User Guide", available both as a published book
https://www.amazon.com/dp/4431554408/?tag=pfamazon01-20
and a free arXiv paper
http://lanl.arxiv.org/abs/1409.3575
That was a true revelation! By rading Natsuume with his brilliant pedagogic style, now I finally start to really understand AdS/CFT. I strongly recommend it to all beginners in AdS/CFT, as the best existing introduction to the subject currently known to me. If you liked Zwiebach for string theory, there are good chances that you will equally like Natsuume for AdS/CFT.
 
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Demystifier said:
I've tried many introductions to AdS/CFT, including the ones mentioned above, but until recently neither of them really worked for me. They all created more confusion than understanding to me.

But a few days ago I discovered Natsuume's "AdS/CFT Duality User Guide", available both as a published book
https://www.amazon.com/dp/4431554408/?tag=pfamazon01-20
and a free arXiv paper
http://lanl.arxiv.org/abs/1409.3575
That was a true revelation! By rading Natsuume with his brilliant pedagogic style, now I finally start to really understand AdS/CFT. I strongly recommend it to all beginners in AdS/CFT, as the best existing introduction to the subject currently known to me. If you liked Zwiebach for string theory, there are good chances that you will equally like Natsuume for AdS/CFT.
I discovered it last week, I still haven't read through it, I have other books on my reading list.
 
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1. What is AdS/CFT?

AdS/CFT stands for Anti-de Sitter/Conformal Field Theory. It is a duality in theoretical physics that relates two different theories: a gravitational theory in anti-de Sitter space (a type of curved spacetime) and a conformal field theory, which is a type of quantum field theory on the boundary of that spacetime. It is an important concept in understanding the holographic principle and has applications in string theory and quantum gravity.

2. What is the background for AdS/CFT?

The background for AdS/CFT is rooted in the work of Albert Einstein, who developed the theory of general relativity and predicted the existence of anti-de Sitter space. It was further developed by physicists Steven Hawking, Jacob Bekenstein, and Leonard Susskind in their research on the holographic principle. In the late 1990s, Juan Maldacena proposed the AdS/CFT correspondence, which has since been extensively studied and applied in various areas of theoretical physics.

3. How does AdS/CFT work?

AdS/CFT works by relating two seemingly different theories using the holographic principle. The gravitational theory in anti-de Sitter space is described by Einstein's theory of general relativity, while the conformal field theory on the boundary of that spacetime is described by a quantum field theory. The duality states that the two theories are equivalent, meaning they contain the same physical information and can be used to describe the same physical phenomena.

4. What are the applications of AdS/CFT?

AdS/CFT has been used to study various problems in theoretical physics, including black holes, quantum gravity, and high-energy physics. It has also been applied to condensed matter systems, such as superconductors and strongly correlated electron systems. Additionally, AdS/CFT has been used to study the properties of quark-gluon plasma, a state of matter that existed in the early universe and can be recreated in high-energy particle colliders.

5. What are the current challenges in AdS/CFT research?

Despite its many successes, AdS/CFT is still a developing field of research, and there are several challenges that scientists are currently facing. These include understanding the microscopic origins of the AdS/CFT duality, resolving the information paradox in black holes, and connecting AdS/CFT to more realistic models of the universe. Additionally, there is ongoing work to extend the applicability of AdS/CFT to other areas of physics, such as condensed matter and cosmology.

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