Chern-Simons and string theory. (English) Zbl 1104.81078

Summary: We discuss a special case of the gauge theory to string theory correspondence where exact results are available. We show how the Witten-Reshetikhin-Turaev invariant in SU\((n)\) Chern-Simons theory on \(S^3\) is related via conifold transition to the all genus generating function of the topological string amplitudes on a Calabi-Yau manifold.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
58J20 Index theory and related fixed-point theorems on manifolds
14J32 Calabi-Yau manifolds (algebro-geometric aspects)