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Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
Інший ID:
2010 Mathematics Subject Classification: 14J32
DOI: http://dx.doi.org/10.3842/SIGMA.2012.088
DOI: http://dx.doi.org/10.3842/SIGMA.2012.088
Посилання:
Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case / B. Szendrői // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 31 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Mirror Symmetry and Related Topics”. The full collection is available at http://www.emis.de/journals/SIGMA/mirror symmetry.html.
I wish to thank Jim Bryan, Lotte Hollands, Dominic Joyce, Davesh Maulik, Geordie Williamson and especially Ian Grojnowski for comments and discussions. This research was supported by EPSRC Programme Grant EP/I033343/1, and by a Fellowship from the Alexander von Humboldt Foundation. Part of this paper was prepared while I was visiting the Department of Mathematics, Freie Universit¨at Berlin; I wish to thank them and especially Klaus Altmann for hospitality.
Дата:
2012
Переглядів:
487
Завантажень:
430
Анотація:
This paper studies geometric engineering, in the simplest possible case of rank one (Abelian) gauge theory on the affine plane and the resolved conifold. We recall the identification between Nekrasov's partition function and a version of refined Donaldson-Thomas theory, and study the relationship between the underlying vector spaces. Using a purity result, we identify the vector space underlying refined Donaldson-Thomas theory on the conifold geometry as the exterior space of the space of polynomial functions on the affine plane, with the (Lefschetz) SL(2)-action on the threefold side being dual to the geometric SL(2)-action on the affine plane. We suggest that the exterior space should be a module for the (explicitly not yet known) cohomological Hall algebra (algebra of BPS states) of the conifold.
