Topological Strings and Integrable Hierarchies

  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},
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… 

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