Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes

Details Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes

2003-12-19

arxiv.org/abs/hep-th/0312234v3

Phys.Lett. B585 (2004) 163-172

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 2 figures, (v2,3) minor changes, to appear in Phys. Lett. B

Scientific paper

10.1016/j.physletb.2004.01.085

We consider the geometric transition and compute the all-genus topological string amplitudes expressed in terms of Hopf link invariants and topological vertices of Chern-Simons gauge theory. We introduce an operator technique of 2-dimensional CFT which greatly simplifies the computations. We in particular show that in the case of local Calabi-Yau manifolds described by toric geometry basic amplitudes are written as vacuum expectation values of a product vertex operators and thus appear quite similar to the Veneziano amplitudes of the old dual resonance models. Topological string amplitudes can be easily evaluated using vertex operator algebra.

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