Quantum Barnes Function as the Partition Function of the Resolved Conifold
We give a short new proof of large N duality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold. Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/438648 |
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| _version_ | 1832562443207835648 |
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| author | Sergiy Koshkin |
| author_facet | Sergiy Koshkin |
| author_sort | Sergiy Koshkin |
| collection | DOAJ |
| description | We give a short new proof of large N duality between the Chern-Simons invariants
of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of
the resolved conifold. Our strategy applies to more general situations, and it is
to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons
invariants as different characterizations of the same holomorphic function. For the
resolved conifold, this function turns out to be the quantum Barnes function, a
natural q-deformation of the classical one that in its turn generalizes the Euler
gamma function. Our reasoning is based on a new formula for this function that
expresses it as a graded product of q-shifted multifactorials. |
| format | Article |
| id | doaj-art-0b4c4ec8524e4174b31de316225e1b00 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0b4c4ec8524e4174b31de316225e1b002025-02-03T01:22:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/438648438648Quantum Barnes Function as the Partition Function of the Resolved ConifoldSergiy Koshkin0Department of Mathematics, Northwestern University, Evanston, IL 60208, USAWe give a short new proof of large N duality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold. Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons invariants as different characterizations of the same holomorphic function. For the resolved conifold, this function turns out to be the quantum Barnes function, a natural q-deformation of the classical one that in its turn generalizes the Euler gamma function. Our reasoning is based on a new formula for this function that expresses it as a graded product of q-shifted multifactorials.http://dx.doi.org/10.1155/2008/438648 |
| spellingShingle | Sergiy Koshkin Quantum Barnes Function as the Partition Function of the Resolved Conifold International Journal of Mathematics and Mathematical Sciences |
| title | Quantum Barnes Function as the Partition Function of the Resolved Conifold |
| title_full | Quantum Barnes Function as the Partition Function of the Resolved Conifold |
| title_fullStr | Quantum Barnes Function as the Partition Function of the Resolved Conifold |
| title_full_unstemmed | Quantum Barnes Function as the Partition Function of the Resolved Conifold |
| title_short | Quantum Barnes Function as the Partition Function of the Resolved Conifold |
| title_sort | quantum barnes function as the partition function of the resolved conifold |
| url | http://dx.doi.org/10.1155/2008/438648 |
| work_keys_str_mv | AT sergiykoshkin quantumbarnesfunctionasthepartitionfunctionoftheresolvedconifold |