Quantum Barnes function as the partition function of the resolved conifold

TL;DR

The paper introduces the quantum Barnes function as a unifying holomorphic function representing Gromov-Witten, Donaldson-Thomas, and Chern-Simons invariants of the resolved conifold, providing a new approach to large N duality.

Contribution

It presents a novel interpretation of these invariants through the quantum Barnes function and offers a new formula expressing it as a graded product of q-shifted multifactorials.

Findings

Quantum Barnes function as the partition function of the resolved conifold

New formula expressing the function as a graded product of q-shifted multifactorials

Unified perspective on invariants via the quantum Barnes function

Abstract

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.