Mirror symmetry, Langlands duality, and the Hitchin system

Details Mirror symmetry, Langlands duality, and the Hitchin system Mirror symmetry, Langlands duality, and the Hitchin system

2002-05-23

arxiv.org/abs/math/0205236v1

Mathematics

Algebraic Geometry

31 pages, LaTeX with packages amsfonts, latexsym, [dvips]graphicx, [dvips]color, one embedded postscript figure

Scientific paper

10.1007/s00222-003-0286-7

We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different senses. First, they satisfy the requirements laid down by Strominger-Yau-Zaslow (SYZ), in a suitably general sense involving a B-field or flat unitary gerbe. To show this, we use their hyperkahler structures and Hitchin's integrable systems. Second, their Hodge numbers, again in a suitably general sense, are equal. These spaces provide significant evidence in support of SYZ. Moreover, they throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.

Affiliated with

Also associated with

No associations

Rating

Mirror symmetry, Langlands duality, and the Hitchin system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mirror symmetry, Langlands duality, and the Hitchin system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mirror symmetry, Langlands duality, and the Hitchin system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-454525