Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-27
Nucl.Phys. B678 (2004) 656-681
Physics
High Energy Physics
High Energy Physics - Theory
Some clarifications added. Final version to appear in NPB
Scientific paper
Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on $S^3$. These three-manifold invariants are proportional to the trivial connection contribution to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large $N$ expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string $A$-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds.
Borhade Pravina
Ramadevi P.
Sarkar Tapobrata
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