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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148611 |
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| Cite this: | 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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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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications q -Difference Kac-Schwarz Operators in Topological String Theory Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
q -Difference Kac-Schwarz Operators in Topological String Theory |
| spellingShingle |
q -Difference Kac-Schwarz Operators in Topological String Theory Takasaki, K. Nakatsu, T. |
| 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 |
| author |
Takasaki, K. Nakatsu, T. |
| author_facet |
Takasaki, K. Nakatsu, T. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
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AT takasakik qdifferencekacschwarzoperatorsintopologicalstringtheory AT nakatsut qdifferencekacschwarzoperatorsintopologicalstringtheory |
| first_indexed |
2025-12-07T19:47:17Z |
| last_indexed |
2025-12-07T19:47:17Z |
| _version_ |
1850880124030812160 |