Gopakumar, Ooguri and Vafa famously proposed the existence of a correspondence between a topological gauge theory on one hand ($U(N)$ Chern-Simons theory on the three-sphere) and a topological string theory on the other (the topological A-model on the resolved conifold). On the physics side, this duality provides a concrete instance of the large $N$ gauge/string correspondence where exact computations can be performed in detail; mathematically, it puts forward a triangle of striking relations between quantum invariants (Reshetikhin-Turaev-Witten) of knots and 3-manifolds, curve-counting invariants (Gromov-Witten/Donaldson-Thomas) of local Calabi-Yau 3-folds, and the Eynard-Orantin recursion for a specific class of spectral curves. I quickly survey recent results on the most general frame of validity of this correspondence and discuss some of its implications.
|Publication status||Published - 20 Nov 2017|
|Event||2016 AMS von Neumann Symposium: Topological Recursion and its Inﬂuence in Analysis, Geometry, and Topology - Hilton Charlotte University Place, Charlotte, United States|
Duration: 4 Jul 2016 → 8 Jul 2016
|Conference||2016 AMS von Neumann Symposium|
|Period||4/07/16 → 8/07/16|
Bibliographical noteWrite-up of a talk at the AMS Von Neumann symposium 2016, meant as a short survey, with a more physical slant, of arXiv:1506.06887 and Section 4.2 of arXiv:1711.05958 to which the reader is referred for the original material and more details.