After complaining bitterly about my lack of free time, at least now I have finished writting the first paper of the year, so now I can show some of the work I’ve been doing. I’ve been feeling so overworked that at least I can celebrate the small accomplishments of the day. This is why, if I write a paper, I tell my family about it and have little celebrations. These are like drinking a nice glass of wine with dinner, or doing other silly little things to show my good mood.
It feels good to let go! There is still the apprehension of what will people say. But after writing so many papers, you kind of get used to it. Considering that from gestation of ideas, to calculations, to a paper it took more than 9 months, it’s not that different in time scale from delivering a baby. Seeing that it is only 4 pages, it doesn’t seem like it would take so much effort.
The paper is short and sweet, but rather technical and you can find it here. To tell the truth, I only expect the experts in the field to understand it fully. I believe the paper delivers a punch.
I had a great collaborator working with me, Diego Trancanelli. He is a postdoc at UCSB.
The difficulty for reading the paper is that we use some techniques that are not broadly well known, and even though the calculations can be done on the back of an envelope, a full justification of why you can do them this way is rather longwinded (it really takes me an hour talking to experts in a seminar to get the point across, and I’ve spent a few years developing some of the tools that are used). I’m very happy with the end result, which for the most part proves a rather hard statement, so long as one accepts the premise of the calculations.
Now, for complicated jargon’s sake, I think it would be too much to expect that the general readers of this blog would know what S-duality, N=4 SYM, matrix models, central charges and planar diagrams are. So if I say that one can combine them into statements about (p,q)-string giant magnons and their dispersion relation I believe most would not follow me. The giant magnon dispersion relation has a functional form dictated by integrable structures, but there is an in-principle unknown function of the coupling constants that one has to determine. We showed that the currently conjectured answer in the literature is the only possibility that is compatible with all the non-perturbative symmetries and dependences that one needs. One can call it a non-renormalization theorem (but explaining what that means takes even more time).
We managed to do that by expanding around strong coupling (this is rather different than other non-renormalization theorems). This is why everything is so unconventional.
This is the end of the blog-release on the paper. (Is that how you call it?– I call it a bit of self-promotion and a good opportunity for catharsis.) Read it if you dare. This post is part of my small celebration for the occasion. Now I have to go hide again and prepare class for tomorrow.