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We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the… (More)

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix… (More)

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic… (More)

Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for N = 2 quantum field theories can be reduced to T-dualities of… (More)

We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries, including the mirrors of toric manifolds. The formalism is based on… (More)

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau… (More)

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods ofX . This acts on the topological string wave function in a natural… (More)

We show how the Riemann surface Σ of N = 2 Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE… (More)

We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from… (More)

We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which… (More)