The transparencies from the conference on twistor string theory held two weeks ago at Oxford are now available on-line.
Quite a few of the talks deal with the technical details of computing amplitudes. For the motivation from phenomenological particle theory, see the talk by Zvi Bern. As for the motivation and present state of the whole idea of relating QCD to a string theory in twistor space, the only person who really seems to have much to say about this is Witten himself. His transparencies are in three parts: part 1a and part 1b from his first talk and then a second talk in which he explains what the problems with the whole idea are and some ideas he’s been thinking about using to try and get around them.
Related to Atiyah’s notes is the following very interesting paper:
http://arxiv.org/PS_cache/hep-th/pdf/0105/0105179.pdf
-drl
I’ve been meaning to look into this question…
Since one apparently invokes twistors to get some knowledge of spacetime (M), is there a technical reason one must build on SO(4,2) vs. SO(3,3)? All the ideas of incidence will hold, with suitable replacement of real configurations by imaginary ones. Of course one will lose the real scalings in M but we don’t experience these in any case.
-drl
[...] Zvi Bern gave a talk yesterday at the KITP in Santa Barbara entitled The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity. He surveyed recent progress on computing perturbative amplitudes in QCD and N=4 supersymmetric Yang-Mills, some of which involves using twistor methods. The most striking thing though were his last few transparencies (here, here, and here). He notes that all previous studies of divergences in supergravity rely only on power-counting and supersymmetry, assuming that if these two principles allow a divergence to occur, it will. Actually doing the full computation to see if the divergences are there is too hard and no one has done it. Bern notes that in these arguments the extra structure seen by the recent twistor methods is not taken into account, and when one does this, so far all complete calculations show that N=8 supergravity has exactly the same degree of divergence as N=4 Yang-Mills, even though one would naively expect the supergravity amplitudes to have worse behavior. He ends by suggesting that “Serious re-examination of the UV properties of multi-loop N=8 supergravity using modern tools is needed.” [...]