A note -- when linking to arXiv, please link to the abstract[1], not directly to the PDF. The abstract has other information about the paper, and one can see different versions of the paper, and of course one can click through to the actual paper. Going the other way requires manually editing the URL.

[1]http://arxiv.org/abs/1212.5605v1

(non physicist, non mathematician) The current excitement seems to be to do with a forthcoming paper from Arkani Hamed and his student Jaroslav Trnka. The pdf at http://www.staff.science.uu.nl/~tonge105/igst13/Trnka.pdf has some details of that, I think.

Edit to add:

The pdf is slides from a talk by Trnka. Video of a later talk on the same topic by Arkani Hamed is at http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha... - he sounds very excited!

I was talking to a friend in the physics department at Stanford a few months ago about how one of the people whose work is cited in this paper (Greg Moore of Rutgers) had found analytic expressions purely rooted in geometry for Bethe Ansatz[1] results in (1+1) dimensional systems. Based on that, I told my friend I believed these "physical mathematics types" (as they call themselves) were on to something. He concurred that their methods would be very important in the future.

(This was in May, lol)

[1] BA is a nifty numerical method involving a lot of number crunching to find scattering matrices for these theories, and is very useful in low-dimensional electronic systems.

I think there's a lot of exciting research going on in the context of integrable systems (~Bethe Ansatz) and N=2 quantum field theories. However, some people are also working on integrability in N=4 theories, which might be relevant to the ideas in this article. It's a thought some people (including Arkani-Hamed) have expressed, but it's too early to tell.

You don't know any of Neitzke's grad students by any chance, do you? A certain fellow with a fondness for army boots and camo fatigues used to live down the hall from me at Caltech....

A certain fellow working down the hall from me is quirky enough to match that description :-)

The point was that these techniques that people are decrying as just applying to super idealized cases in N=4 SUSY produced real computationally and experimentally testable results in real lower dimensional systems. However, no one is going to be putting out excited press releases about thermodynamic Bethe Ansaetze.

Thanks for clarifying. That it's not limited idealized cases is a very good point, and my apologies for my earlier snarky comment.

And here's a (long!) recent review about developments in this area over the past few years -- http://arxiv.org/abs/1308.1697