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q -Difference Kac-Schwarz Operators in Topological String Theory

q -Difference Kac-Schwarz Operators in Topological String Theory

The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web diagram of such geometry can be packed into a multi-varia...

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Main Authors: Takasaki, K., Nakatsu, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148611
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spelling irk-123456789-1486112019-02-19T01:25:03Z q -Difference Kac-Schwarz Operators in Topological String Theory Takasaki, K. Nakatsu, T. The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web diagram of such geometry can be packed into a multi-variate generating function. This generating function turns out to be a tau function of the KP hierarchy. The tau function has a fermionic expression, from which one finds a vector |W⟩ in the fermionic Fock space that represents a point W of the Sato Grassmannian. |W⟩ is generated from the vacuum vector |0⟩ by an operator g on the Fock space. g determines an operator G on the space V=C((x)) of Laurent series in which W is realized as a linear subspace. 2017 Article q -Difference Kac-Schwarz Operators in Topological String Theory / K. Takasaki, T. Nakatsu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 67 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 39A13; 81T30 DOI:10.3842/SIGMA.2017.009 http://dspace.nbuv.gov.ua/handle/123456789/148611 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web diagram of such geometry can be packed into a multi-variate generating function. This generating function turns out to be a tau function of the KP hierarchy. The tau function has a fermionic expression, from which one finds a vector |W⟩ in the fermionic Fock space that represents a point W of the Sato Grassmannian. |W⟩ is generated from the vacuum vector |0⟩ by an operator g on the Fock space. g determines an operator G on the space V=C((x)) of Laurent series in which W is realized as a linear subspace.
format Article
author Takasaki, K.
Nakatsu, T.
spellingShingle Takasaki, K.
Nakatsu, T.
q -Difference Kac-Schwarz Operators in Topological String Theory
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Takasaki, K.
Nakatsu, T.
author_sort Takasaki, K.
title q -Difference Kac-Schwarz Operators in Topological String Theory
title_short q -Difference Kac-Schwarz Operators in Topological String Theory
title_full q -Difference Kac-Schwarz Operators in Topological String Theory
title_fullStr q -Difference Kac-Schwarz Operators in Topological String Theory
title_full_unstemmed q -Difference Kac-Schwarz Operators in Topological String Theory
title_sort q -difference kac-schwarz operators in topological string theory
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/148611
citation_txt q -Difference Kac-Schwarz Operators in Topological String Theory / K. Takasaki, T. Nakatsu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 67 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT takasakik qdifferencekacschwarzoperatorsintopologicalstringtheory
AT nakatsut qdifferencekacschwarzoperatorsintopologicalstringtheory
first_indexed 2023-05-20T17:29:45Z
last_indexed 2023-05-20T17:29:45Z
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