Non-compact Topological Branes on Conifold

TL;DR

This paper investigates non-compact branes in topological string theories on Calabi-Yau spaces, computing their amplitudes across different models and confirming their wavefunction behavior and large N duality consistency.

Contribution

It provides a comprehensive analysis of non-compact brane amplitudes in A-model, B-model, and matrix model frameworks, demonstrating their agreement and wavefunction properties.

Findings

Amplitudes agree across A-model, B-model, and matrix model descriptions.

Non-compact brane amplitudes obey Schrödinger equation, confirming wavefunction behavior.

Results support large N duality and clarify the role of symmetries in these models.

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 Schr\"odinger 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.