Flop Invariance of Refined Topological Vertex and Link Homologies

Details Flop Invariance of Refined Topological Vertex and Link Homologies Flop Invariance of Refined Topological Vertex and Link Homologies

2008-05-03

arxiv.org/abs/0805.0336v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 3 figures

Scientific paper

It has been proposed recently that the topological A-model string theory on local toric Calabi-Yau manifolds has a two parameter extension. Amplitudes of the two parameter topological strings can be computed using a diagrammatic method called the refined topological vertex. In this paper we study properties of the refined amplitudes under the flop transition of toric Calabi-Yau three-folds. We also discuss that the slicing invariance and the flop transition imply a simple formula for the homological sl(N) invariants of the Hopf link. The new expression for the invariants gives a simple refinement of the Hopf link invariant of Chern-Simons theory.

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