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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2017
Hauptverfasser: Takasaki, K., Nakatsu, T.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148611
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Takasaki, K.
Nakatsu, T.
author_facet Takasaki, K.
Nakatsu, T.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
first_indexed 2025-12-07T19:47:17Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T19:47:17Z
publishDate 2017
publisher Інститут математики НАН України
record_format dspace
spelling Takasaki, K.
Nakatsu, T.
2019-02-18T16:34:02Z
2019-02-18T16:34:02Z
2017
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
https://nasplib.isofts.kiev.ua/handle/123456789/148611
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.
The authors are grateful to Motohico Mulase for discussion and encouragement. We owe him
 the idea that an integrable hierarchy may be thought of as a mirror map. This work is partly
 supported by JSPS Kakenhi Grant No. 25400111 and No. 15K04912.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
q -Difference Kac-Schwarz Operators in Topological String Theory
Article
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spellingShingle q -Difference Kac-Schwarz Operators in Topological String Theory
Takasaki, K.
Nakatsu, T.
title 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_short q -Difference Kac-Schwarz Operators in Topological String Theory
title_sort q -difference kac-schwarz operators in topological string theory
url https://nasplib.isofts.kiev.ua/handle/123456789/148611
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