Quantum Barnes function as the partition function of the resolved conifold

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Koshkin, Sergiy
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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.
Comment: 47 pages, 7 figures
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Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematics - Quantum Algebra, 14J32, 14N35, 57M27, 57R56, 81T45
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