Mirror symmetry, Langlands duality, and the Hitchin system
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 S...
المؤلفون الرئيسيون: | , |
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التنسيق: | Journal article |
اللغة: | English |
منشور في: |
2002
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_version_ | 1826273946071203840 |
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author | Hausel, T Thaddeus, M |
author_facet | Hausel, T Thaddeus, M |
author_sort | Hausel, T |
collection | OXFORD |
description | 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. |
first_indexed | 2024-03-06T22:35:57Z |
format | Journal article |
id | oxford-uuid:59e7848a-ffcb-41b7-ad5d-f42d5a927d35 |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-06T22:35:57Z |
publishDate | 2002 |
record_format | dspace |
spelling | oxford-uuid:59e7848a-ffcb-41b7-ad5d-f42d5a927d352022-03-26T17:12:24ZMirror symmetry, Langlands duality, and the Hitchin systemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:59e7848a-ffcb-41b7-ad5d-f42d5a927d35EnglishSymplectic Elements at Oxford2002Hausel, TThaddeus, MWe 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. |
spellingShingle | Hausel, T Thaddeus, M Mirror symmetry, Langlands duality, and the Hitchin system |
title | Mirror symmetry, Langlands duality, and the Hitchin system |
title_full | Mirror symmetry, Langlands duality, and the Hitchin system |
title_fullStr | Mirror symmetry, Langlands duality, and the Hitchin system |
title_full_unstemmed | Mirror symmetry, Langlands duality, and the Hitchin system |
title_short | Mirror symmetry, Langlands duality, and the Hitchin system |
title_sort | mirror symmetry langlands duality and the hitchin system |
work_keys_str_mv | AT hauselt mirrorsymmetrylanglandsdualityandthehitchinsystem AT thaddeusm mirrorsymmetrylanglandsdualityandthehitchinsystem |