Quantum Barnes Function as the Partition Function of the Resolved Conifold
نویسنده
چکیده
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 DonaldsonThomas, 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.
منابع مشابه
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2008 شماره
صفحات -
تاریخ انتشار 2008