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SIGMA, 2012, Volume 8, 088, 16 pages (Mi sigma765)  

This article is cited in 4 scientific papers (total in 4 papers)

Nekrasov's Partition Function and Refined Donaldson–Thomas Theory: the Rank One Case

Balázs Szendrői

Mathematical Institute, University of Oxford, UK

Abstract: 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) $\mathrm{SL}(2)$-action on the threefold side being dual to the geometric $\mathrm{SL}(2)$-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.

Keywords: geometric engineering; Donaldson–Thomas theory; resolved conifold

DOI: https://doi.org/10.3842/SIGMA.2012.088

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Full text: http://emis.mi.ras.ru/.../088
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Bibliographic databases:

ArXiv: 1210.5181
MSC: 14J32
Received: June 12, 2012; in final form November 5, 2012; Published online November 17, 2012
Language:

Citation: Balázs Szendrői, “Nekrasov's Partition Function and Refined Donaldson–Thomas Theory: the Rank One Case”, SIGMA, 8 (2012), 088, 16 pp.

Citation in format AMSBIB
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\by Bal\'azs~Szendr{\H o}i
\paper Nekrasov's Partition Function and Refined Donaldson--Thomas Theory: the~Rank One Case
\jour SIGMA
\yr 2012
\vol 8
\papernumber 088
\totalpages 16
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\crossref{https://doi.org/10.3842/SIGMA.2012.088}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nakajima H., “Refined Chern-Simons Theory and Hilbert Schemes of Points on the Plane”, Perspectives in Representation Theory: a Conference in Honor of Igor Frenkel'S 60Th Birthday on Perspectives in Representation Theory, Contemporary Mathematics, 610, eds. Etingof P., Khovanov M., Savage A., Amer Mathematical Soc, 2014, 305–331  crossref  mathscinet  zmath  isi
    2. Ben Davison, Maulik D., Schuermann J., Szendroi B., “Purity For Graded Potentials and Quantum Cluster Positivity”, Compos. Math., 151:10 (2015), 1913–1944  crossref  mathscinet  zmath  isi  scopus
    3. Hayashi H., Piazzalunga N., Uranga A.M., “Towards a Gauge Theory Interpretation of the Real Topological String”, Phys. Rev. D, 93:6 (2016), 066001  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. Szendroi B., “Cohomological Donaldson-Thomas Theory”, String-Math 2014, Proceedings of Symposia in Pure Mathematics, 93, eds. Bouchard V., Doran C., MendezDiez S., Quigley C., Amer Mathematical Soc, 2016, 363+  crossref  mathscinet  zmath  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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