Vertex Operators, ${\mathbb{C}}^3$ Curve and Topological Vertex

Abstract

In this article, we prove the conjecture that Kodaira-Spencer theory for the topological vertex is a free fermion theory. By dividing the ${\mathbb{C}}^3$ curve into core and asymptotic regions and using Boson-Fermion correspondence, we construct a generic three-leg correlation function which reformulates the topological vertex in a vertex operator approach. We propose a conjecture of the correlation function identity which in a degenerate case becomes Zhou\rq{}s identity for a Hopf link.

28 pages, 2 figures

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