International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 438648, 47 pages
doi:10.1155/2008/438648

Quantum Barnes function as the partition function of the resolved conifold

Abstract

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.