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

Andrea Brini

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

Andrea Brini

Mathematics

Research output: Contribution to conference (unpublished) › Paper › peer-review

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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.

Original language	English
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 http://www.ams.org/meetings/amsconf/symposia/symposia-2016

Conference

Conference	2016 AMS von Neumann Symposium
Country/Territory	United States
City	Charlotte
Period	4/07/16 → 8/07/16
Internet address	http://www.ams.org/meetings/amsconf/symposia/symposia-2016

Bibliographical 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.

Keywords

hep-th
math-ph
math.MP

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Brini_Gopakumar-Ooguri-Vafa_Symposia in Pure MathematicsAccepted author manuscript, 621 KBLicence: None: All rights reserved

https://arxiv.org/abs/1711.07826

Cite this

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title = "On the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds",

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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AU - Brini, Andrea

N1 - 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.

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Y1 - 2017/11/20

N2 - 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.

AB - 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.

KW - hep-th

KW - math-ph

KW - math.MP

M3 - Paper

T2 - 2016 AMS von Neumann Symposium

Y2 - 4 July 2016 through 8 July 2016

ER -

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

Abstract

Conference

Bibliographical note

Keywords

Access to Document

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Cite this