Quantum Barnes function as the partition function of the resolved conifold

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.

47 pages, 7 figures

References in corpus (4)

• Chern-Simons Theory and Topological Strings
• Zero dimensional Donaldson-Thomas invariants of threefolds
• Universal Character and Large N Factorization in Topological Gauge/String Theory
• A Vertex Formalism for Local Ruled Surfaces

Cited by in corpus (1)

• Conformal TBA for resolved conifolds