# Topological Strings and Integrable Hierarchies

@article{Aganagic2006TopologicalSA, title={Topological Strings and Integrable Hierarchies}, author={Mina Aganagic and Robbert Dijkgraaf and Albrecht Klemm and Marcos Mari{\~n}o and Cumrun Vafa}, journal={Communications in Mathematical Physics}, year={2006}, volume={261}, pages={451-516} }

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using -algebra symmetries which encode the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and…

## 231 Citations

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We study the open B-model representing D-branes on 2-cycles of local Calabi-Yau geometries. To this end we work out a reduction technique linking D-brane partition functions and multimatrix models in…

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We study difference equations which are obtained from the asymptotic expansion of topological string theory on the deformed and the resolved conifold geometries as well as for topological string…

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