# Pedagogic reference for calculation of 2-loop anomalous dimension (supersymmetric)

I want to know of pedagogic references which teach how to compute anomalous dimensions (..wave-function renormalization..) at lets say 2-loops. I guess there might be specialized techniques for supersymmetric theories and especially may be adapted for $2+1$ dimensions.

• I have in mind being able to understand calculations like say in this paper in Appendix D starting on page 39.

I found the treatment of this subject in books like Peskin and Schroeder very sketchy and not explanatory enough. I would like to know of any more detailed "modern" reference which will help lets say with the calculation linked above.

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The case of one-loop (and higher) anomalous dimensions in $\mathcal{N}=4$ SYM is discussed a bit in the recent reviews in arXiv:1012.3983 and arXiv:1012.3984. The same techniques are useful also in the case of supersymmetric Chern-Simons, see eg the two-loop case in arXiv:0806.3951, or the four-loop calculations in arXiv:0912.3460 or arXiv:1010.1756.

(Edit: as Qmechanic pointed out I should of course mention that I'm one of the authors of the last two papers referenced above. I hope they are relevant to the question.)

If you rather want textbooks that give general introductions to the renormalization of local operators I like Collins, "Renormalization" and Kleinert, "Critical properties of $\phi^4$-theories". I'm not sure if they are very modern, but they describe the calculation of renormalization coefficients very explicitly.

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Dear Olof, if you cite yourself it is best if you say so explicitly in your answer, cf. Physics.SE policy and SE policy. –  Qmechanic Jul 31 '12 at 12:44
@Qmechanic: Sorry, I was meaning to add a comment but obviously forgot to do so. Thanks for the reminder :) –  Olof Jul 31 '12 at 16:42
@Olof Thanks for the references. Can you tell me as to which of your references can be used as a starting point to "learn" this technology step by step? Like if you can may be order them in increasing level of difficulty. I am more like looking for a step by step introduction to this method of calculating anomalous dimensions (sypersymmetric may be) which will help me understand the calculation linked to from my question. Can you may be comment as to where in Collis is this?..which part is most suited for this cause? –  user6818 Jul 31 '12 at 21:44
@Anirbit: Unfortunately I don't have Collins book handy, but there should be a chapter about renormalization of local operators (google books tells me it's chapter 6). The papers I mentioned are are not reviews about how to do the calculation, but give some real world examples with quite a lot of detail. –  Olof Aug 1 '12 at 8:45
@olof I was wondering if you could give suggestions about a study route among these 5 papers that you linked to. Like if you could suggest which one would be the starting point/easiest to start with to learn this technology. –  user6818 Aug 1 '12 at 18:53
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