146 research outputs found
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 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
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