uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Physics and geometry of knots-quivers correspondence
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Institut Mittag-Leffler, Aurav 17, 182 60 Djursholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Institute for Theoretical Physics, ETH Zurich, CH - 8093, Zurich, Switzerland.
2018 (English)Manuscript (preprint) (Other academic)
Abstract [en]

The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot K in the 3-sphere to representation theory of a quiver QK associated to the knot. In this paper we provide geometric and physical contexts for this conjecture within the framework of the large N duality of Ooguri and Vafa, that relates knot invariants to counts of holomorphic curves with boundary on LK, the conormal Lagrangian of the knot in the resolved conifold, and corresponding M-theory considerations. From the physics side, we show that the quiver encodes a 3d N=2 theory T[QK] whose low energy dynamics arises on the worldvolume of an M5 brane wrapping the knot conormal and we match the (K-theoretic) vortex partition function of this theory with the motivic generating series of QK. From the geometry side, we argue that the spectrum of (generalized) holomorphic curves on LK is generated by a finite set of basic disks. These disks correspond to the nodes of the quiver QK and the linking of their boundaries to the quiver arrows. We extend this basic dictionary further and propose a detailed map between quiver data and topological and geometric properties of the basic disks that again leads to matching partition functions. We also study generalizations of A-polynomials associated to QK and (doubly) refined version of LMOV invariants.

Place, publisher, year, edition, pages
2018.
National Category
Subatomic Physics
Identifiers
URN: urn:nbn:se:uu:diva-371286OAI: oai:DiVA.org:uu-371286DiVA, id: diva2:1272954
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-05-06Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

https://arxiv.org/abs/1811.03110

Authority records BETA

Ekholm, TobiasLonghi, Pietro

Search in DiVA

By author/editor
Ekholm, TobiasLonghi, Pietro
By organisation
Algebra and GeometryTheoretical Physics
Subatomic Physics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 55 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf