Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
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 relationsh...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148654 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862571681031127040 |
|---|---|
| author | Szendrői, B. |
| author_facet | Szendrői, B. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2025-11-26T05:09:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148654 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T05:09:07Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Szendrői, B. 2019-02-18T17:35:14Z 2019-02-18T17:35:14Z 2012 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. 1815-0659 2010 Mathematics Subject Classification: 14J32 DOI: http://dx.doi.org/10.3842/SIGMA.2012.088 https://nasplib.isofts.kiev.ua/handle/123456789/148654 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case Article published earlier |
| spellingShingle | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case Szendrői, B. |
| title | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case |
| title_full | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case |
| title_fullStr | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case |
| title_full_unstemmed | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case |
| title_short | Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case |
| title_sort | nekrasov's partition function and refined donaldson-thomas theory: the rank one case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148654 |
| work_keys_str_mv | AT szendroib nekrasovspartitionfunctionandrefineddonaldsonthomastheorytherankonecase |