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arXiv · 1711.07826

On the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds

Andrea Brini
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Abstract

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.

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Andrea Brini. 2017-11-20. On the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds. https://arxiv.org/abs/1711.07826

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