U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

Pravina Borhade; P. Ramadevi; Tapobrata Sarkar

doi:10.1016/j.nuclphysb.2003.11.023

paper

U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

arXiv:hep-th/0306283 · doi:10.1016/j.nuclphysb.2003.11.023

Abstract

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.

Some clarifications added. Final version to appear in NPB

References in corpus (1)

N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry

U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

Abstract

References in corpus (1)

Cited by in corpus (15)