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Topological Strings and Integrable Hierarchies

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arxiv hep-th/0312085 v1 pith:JXYYRFP6 submitted 2003-12-09 hep-th

Mina Aganagic , Robbert Dijkgraaf , Albrecht Klemm , Marcos Marino , Cumrun Vafa This is my paper
classification hep-th
keywords topologicalcalabi-yaumatrixamplitudeslocalstringsb-modelgeometries
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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 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 various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.

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Cited by 6 Pith papers

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