A talk by Linda Uruchurtu (based on this paper) reviews the study of correlation functions in AdS5/CFT4.
correlation functions
November 12, 2011
resources
June 28, 2011
Joseph Minahan has the best introduction to N=4 super-Yang-Mills that I’ve seen.
Slides from Marcus Spradlin at KITP touch on many developments.
Luis Alday reviews the interpretation of scattering amplitudes at strong coupling as a minimal surface in anti-de-Sitter space.
I believe Simon Caron-Huot’s latest is currently the most advanced paper on the subject: a generalization of scattering amplitudes is proposed, that would possess superconformal and dual superconformal symmetry, and which would begin to explain the simplicity recently discovered in the BDS remainder function, as discussed by Spradlin.
pictures from Beisert et al
May 19, 2011
Chapter 1 of the recent epic “Review of AdS/CFT Integrability” by Niklas Beisert and 25 other authors contains two images worth contemplating.
First, the theoretical frameworks employed in different regions of parameter space. 
Second, the techniques used to compute the spectrum of operators in different regions of parameter space. 
The second picture does not map vertically onto the first; it describes calculations in the “planar limit”, which corresponds only to the bottom of the first picture.
From a recent talk at KITP by Nima Arkani-Hamed, I have derived the following model of how progress towards a full solution should proceed: first by calculating the anomalous dimensions of operators (this has been done, and is reviewed in Beisert et al), then by calculating scattering amplitudes (subject of a current KITP workshop), then by calculating correlation functions (currently still in a pre-Parke-Taylor condition, according to Arkani-Hamed).
I’ve had to teach myself what I know of advanced physics. So while I know more about quantum field theory than the average person, there are gaps in my technical knowledge. On the other hand, the culmination of this blog would be to exhibit the exact solution of a particular quantum field theory. Mathematically, that ought to be an object as unambiguous as a multiplication table (though rather more complex). At this time, I’m not even sure what that “exact solution” would look like – maybe a listing of all the n-point correlation functions?
So one theme of the blog will be the struggle to clarify the basic concepts. I won’t entirely avoid talking about matters for which I only have an informal understanding; but I will be especially interested in functions, structures, relations that I can write down completely and unambiguously – like that multiplication table. Once we have the table, we can still have philosophical debates about what multiplication is, and what numbers are; but once we have the table, and the principle of its construction, we are done with the quantitative part of the problem. The object we are seeking – the solution of N=4 super-Yang-Mills – is a quantitative object. There will be plenty of opportunities for conceptual and even metaphysical discussion as to what it is and what it means, but significant progress will be measured by a growth in my ability to exhibit the numbers, however it is that we frame them.
I will also add that this is not a blog about how I personally solved Yang-Mills theory. I am coming from too far behind; this is mostly an exercise in catching up with what other people have done.
This blog exists in order to discuss progress towards the complete solution of d=4 N=4 super-Yang-Mills theory, an interacting quantum field theory.
