2003/12/09 by Mina Aganagic, Robbert Dijkgraaf, Albrecht Klemm +2 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/s00220-005-1448-9
published as Commun.Math.Phys. 261 (2006) 451-516 · 82 pages, harvmac, 1 figure
arxiv created 2003/12/09 · arxiv updated 2015/06/26
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 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.