Saturday, June 18, 2011

Kapustin on SYM, Mirror Symmetry and Langlands, I

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)

1 comment:

  1. As a survey of Kapustin-Witten, the following preprint by Kapustin is my favorite because it is very compact.

    A 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.

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