How much of QFT/RG before going to CFT?

[IRobot]

Hi,

I have currently working knowledge of basic QFT and Renormalization Group, I digested the first two parts of Peskin Schroeder's book (+ gauge theories construction) and I would like to start learning Conformal Field Theory, do you think I am ready for it? If no, what should I learn before? I'd like to be sure on those points, cause I don't give up really easily so I may end up spending weeks on the firsts chapter of a CFT book, before coming frustrated on QFT. By the way, which book would you recommend? I've seen that there are two classics Senechal Di Francesco Mathieu on one side and Ketov on the other, but which one is the best for a newcomer. Thanks.

I am not sure this is right section to ask, so feel free to move it if necessary.

 

[xepma]

Long story short: start diving into CFT.

The approach taken in CFT is very different from what you will find in standard field theory books. CFT has such a rigid structure, that we can bypass a lot of the simplifications which are usually made in other field theories. So a lot of that machinery is absent in CFT.

So you don't need things like Feynman diagrams -- perturbation theory doesn't apply to CFT. Beta functions are trivial for CFTs, since CFTs are (by definition!) invariant under RG transformations. You'll never need to compute those awful loop diagrams. There are some gauge theory formulations, but not of the Yang-Mills type.

So you might wonder -- well, what's left? Quite a bit actually. There is a huge emphasis on symmetry considerations -- Ward identities are very important for instance.

Start by reading chapter 2 of Di Francesco. It gives a rough overview of the QFT you will need, and you should be familiar with most of the topics (maybe not the Belifante Tensor). If you are comfortable with this chapter, then you are ready for the rest of the book. Chapter 4, 5 and 6 are the basics of CFT. Chapter 7, 8 and 9 go a bit further, but this is where the real stuff starts.

Now, Di Francesco is huge and treats a lot of topics that you can skip over, unless you want to become a complete expert in the field (which takes years). So I suggest you look at other sources such as Ginsparg ( http://arxiv.org/abs/hep-th/9108028 ) and the book by Blumenhagen and Plauschinn. Don't bother with Ketov; it's a little too advanced. The reason is that CFT is sometimes combined with other symmetries (supersymmetry, topological field theories, certain gauge groups) and Ketov spends a lot of time on this -- but you should focus on the basics first.

If you are interested in string theory then I also suggest the book by Polchinski -- String Theory Vol 1. It has a nice overview on CFT.

 

[IRobot]

Thanks just read it, but still pretty useful. So far I was using David Tong's notes on CFT from his String Theory Lecture and Polchinsky's book.