Japanese version
About four years ago, "Kapustin on SYM, Mirror Symmetry and Langlands, I" was posted by Mr. Urs Schreiber, which was based on the lecture by Mr. J.Teschner. I also translated it into Japanese three years ago and posted on my BLOG the last September. I will post II and III as the continues of this article. Perhaps this is the simplest introduction to the famous paper by Witten and Kapustin, "Electric-Magnetic Duality And the Geometric Langlands Program" (arxiv:hep-th/0604151).
The original article:
Kapustin on SYM, Mirror Symmetry and Langlands, I（in English)
A translation into Japanese:
Kapustin on SYM, Mirror Symmetry and Langlands, I（in Japanese)
As a survey of Kapustin-Witten, the following preprint by Kapustin is my favorite because it is very compact.
ReplyDeleteA NOTE ON QUANTUM GEOMETRIC LANGLANDS DUALITY, GAUGE THEORY, AND QUANTIZATION OF THE MODULI SPACE OF FLAT CONNECTIONS arXiv:0811.3264v1
Its chapters are:
1. Introduction
2. GL-twisted theory at t = 0
3. Reduction to two dimensions
4. From A-branes to noncommutative B-branes
5. From noncommutative B-branes to twisted D-modules
6. Line and surface operators at t = 0.
And its background is described in the preprint by Witten
MIRROR SYMMETRY, HITCHIN’S EQUATIONS, AND LANGLANDS DUALITY arXiv:0802.0999v1 [math.RT]
I think that this might be prefered by mathematician.