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Mirror symmetry, Langlands duality, and the Hitchin system

Abstract:

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 ...

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Publication status:
Published

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Publisher copy:
10.1007/s00222-003-0286-7

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Thaddeus, M More by this author
Journal:
INVENTIONES MATHEMATICAE
Volume:
153
Issue:
1
Pages:
197-229
Publication date:
2002-05-23
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
URN:
uuid:59e7848a-ffcb-41b7-ad5d-f42d5a927d35
Source identifiers:
21054
Local pid:
pubs:21054

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