Quantum Barnes Function as the Partition Function of the Resolved Conifold

Quantum Barnes Function as the Partition Function of the Resolved Conifold

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We give a short new proof of large N duality citronella horse shampoo 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, offworld drum pads 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.