Hemisphere partition function and analytic continuation to the conifold point

Barnes function as the partition function of the resolved conifold

We suggest a new strategy for proving large N duality by interpreting GromovWitten, 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 qdeformation of the classical one that in its turn generalizes Euler’s gamma funct...

Quantum Barnes Function as the Partition Function of the Resolved Conifold

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 resolve...

Analytic Continuation of Massless Two-Loop Four-Point Functions

We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like 1→ 3 decay to Minkowskian regions relevant to all 1→ 3 and 2→ 2 reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix ele...

Analytic Continuation of the Resolvent

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work [9] we described the resolvent, and specifically the asymptotic behavior of the Green’s function, on SL(3)/ SO(3) using methods from three-particle scattering....

Green currents and analytic continuation