Quantum Barnes function as the partition function of the resolved conifold

Details Quantum Barnes function as the partition function of the resolved conifold Quantum Barnes function as the partition function of the resolved conifold

2007-10-15

arxiv.org/abs/0710.2929v1

Mathematics

Algebraic Geometry

47 pages, 7 figures

Scientific paper

We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold 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 Euler's gamma function. Our reasoning is based on a new formula for this function that expresses it as a graded product of $q$-shifted multifactorials.

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