Quantum topology and curve counting invariants - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Quantum topology and curve counting invariants

Résumé

Gopakumar, Ooguri and Vafa famously proposed the existence of a correspondence between a topological gauge theory – U (N) Chern–Simons theory on the three-sphere – on one hand, and a topo-logical string theory – the topological A-model on the resolved conifold – on the other. 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 invari-ants (Gromov–Witten/Donaldson–Thomas) of local Calabi-Yau 3-folds, and the Eynard–Orantin recursion for a specific class of spectral curves. I here survey recent results on the most general frame of validity of the strongest form of this correspondence and discuss some of its implications.
Fichier principal
Vignette du fichier
brini_AMS2016.pdf (444.32 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01474196 , version 1 (22-02-2017)

Identifiants

  • HAL Id : hal-01474196 , version 1

Citer

Andrea Brini. Quantum topology and curve counting invariants. 2017. ⟨hal-01474196⟩
187 Consultations
381 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More