- Topological strings and integrable hierarchies
- Communications in Mathematical Physics
- Volume | Issue number
- 261 | 2
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Institute for Theoretical Physics Amsterdam (ITFA)
Korteweg-de Vries Institute for Mathematics (KdVI)
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using MediaObjects/s00220-005-1448-9flb1.gif-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 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 an A-model topological string on P1 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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