Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials

dc.contributor.author

Ekholm, Tobias

dc.contributor.author

Ng, Lenhard

dc.date.accessioned

2018-12-11T15:20:12Z

dc.date.available

2018-12-11T15:20:12Z

dc.date.updated

2018-12-11T15:20:12Z

dc.description.abstract

We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We present an argument that the HOMFLY-PT wave function is determined from SFT by induction on Euler characteristic, and also show how to, more directly, extract its recursion relation by elimination theory applied to finitely many noncommutative equations. The latter can be viewed as the higher genus counterpart of the relation between the augmentation variety and Gromov-Witten disk potentials established by Aganagic, Vafa, and the authors, and, from this perspective, our results can be seen as an SFT approach to quantizing the augmentation variety.

dc.identifier.uri

https://hdl.handle.net/10161/17783

dc.subject

math.SG

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hep-th

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math.GT

dc.title

Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials

dc.type

Journal article

duke.contributor.orcid

Ng, Lenhard|0000-0002-2443-5696

pubs.organisational-group

Trinity College of Arts & Sciences

pubs.organisational-group

Duke

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Mathematics

pubs.publication-status

Submitted

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