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Quantum Barnes Function as the Partition Function of the Resolved Conifold

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  • Sergiy Koshkin

Abstract

We give a short new proof of large 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 -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 -shifted multifactorials.

Suggested Citation

  • Sergiy Koshkin, 2008. "Quantum Barnes Function as the Partition Function of the Resolved Conifold," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-47, March.
    • Handle: RePEc:hin:jijmms:438648
    DOI: 10.1155/2008/438648
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