NDLI: Torus Knots and the Topological Vertex

Content Provider	Springer Nature Link
Author	Klemm, Albrecht Jockers, Hans Soroush, Masoud
Copyright Year	2014
Abstract	We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S $^{3}$. The key role is played by the $${SL(2, \mathbb{Z})}$$ transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S $^{3}$, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi–Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.
Ending Page	989
Page Count	37
Starting Page	953
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	8
Volume Number	104
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-03-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	topological strings Theoretical, Mathematical and Computational Physics Topological field theories Lagrangian submanifolds topological vertex Statistical Physics, Dynamical Systems and Complexity Knots and links in $S^3$ Lagrangian submanifolds; Maslov index Geometry Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants Special curves and curves of low genus local mirror symmetry Invariants of knots and 3-manifolds Group Theory and Generalizations knots Mirror symmetry
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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