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

Research output: Contribution to conference (unpublished)Paperpeer-review

Authors

Colleges, School and Institutes

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.

Bibliographic note

Write-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.

Details

Original languageEnglish
Publication statusPublished - 20 Nov 2017
Event2016 AMS von Neumann Symposium: Topological Recursion and its Influence in Analysis, Geometry, and Topology - Hilton Charlotte University Place, Charlotte, United States
Duration: 4 Jul 20168 Jul 2016
http://www.ams.org/meetings/amsconf/symposia/symposia-2016

Conference

Conference2016 AMS von Neumann Symposium
CountryUnited States
CityCharlotte
Period4/07/168/07/16
Internet address

Keywords

  • hep-th, math-ph, math.MP