Quantum Barnes Function as the Partition Function of the Resolved Conifold

Sergiy Koshkin

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-47

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:438648

DOI: 10.1155/2008/438648

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