On the relation between open and closed topological strings

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.Comment: 28 pages, corrected the proof of eq. 2

Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers

We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint orbits corresponding to the representations assigned to the link components. The large $k$ limit of the integral can be calculated with the help of the stationary phase approximation. The Feynman rules allow us to express the phase in terms of integrals over the manifold and the link components. Its stationary points correspond to flat connections in the link complement. We conjecture a relation between the dominant part of the phase and Milnor's linking numbers. We check it explicitly for the triple and quartic numbers by comparing their expression through the Massey product with Feynman diagram integrals.Comment: 33 pages, 11 figure