Topological Strings and Integrable Hierarchies

Abstract

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.

82 pages, harvmac, 1 figure

References in corpus (7)

• Seiberg-Witten Theory and Random Partitions
• Topological Strings and Nekrasov's formulas
• Localization and Gluing of Topological Amplitudes
• Curve counting and instanton counting
• A Conjecture on Hodge Integrals
• Higher order loop equations for A_r and D_r quiver matrix models
• Hodge Integrals and Integrable Hierarchies

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