Non-compact Topological Branes on Conifold

Abstract

We consider non-compact branes in topological string theories on a class of Calabi-Yau spaces including the resolved conifold and its mirror. We compute the amplitudes of the insertion of non-compact Lagrangian branes in the A-model on the resolved conifold in the context of the topological vertex as well as the melting crystal picture. They all agree with each other and also agree with the results from Chern-Simons theory, supporting the large N duality. We find that they obey the Schrödinger equation confirming the wavefunction behavior of the amplitudes. We also compute the amplitudes of the non-compact B-branes in the DV matrix model which arises as a B-model open string field theory on the mirror manifold of the deformed conifold. We take the large N duality to consider the B-model on the mirror of the resolved conifold and confirm the wave function behavior of this amplitude. We find appropriate descriptions of non-compact branes in each model, which give complete agreements among those amplitudes and clarify the salient features including the role of symmetries toward these agreements.

32 pages, 9 figures, a reference added, typos fixed

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Cited by in corpus (11)

• Open string amplitudes and large order behavior in topological string theory
• Non-commutative Donaldson-Thomas theory and the conifold
• Exponential Networks, WKB and Topological String
• The Volume Conjecture and Topological Strings
• Instanton Counting and Matrix Model
• Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
• Polynomial solution of quantum Grassmann matrices
• Open string amplitudes of closed topological vertex
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• q-Deformed Oscillators and D-branes on Conifold
• $q$-Difference Kac-Schwarz Operators in Topological String Theory