Journal of High Energy Physics

, 2013:175 | Cite as

3d analogs of Argyres-Douglas theories and knot homologies

  • Hiroyuki Fuji
  • Sergei Gukov
  • Marko Stošić
  • Piotr Sulkowski
Open Access
Article

Abstract

We study singularities of algebraic curves associated with 3d \( \mathcal{N}=2 \) theories that have at least one global flavor symmetry. Of particular interest is a class of theories TK labeled by knots, whose partition functions package Poincaré polynomials of the Sr -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d \( \mathcal{N}=2 \) theories TK and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in Sr-colored HOMFLY homologies.

Keywords

Supersymmetric gauge theory Duality in Gauge Field Theories ChernSimons Theories Differential and Algebraic Geometry 

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Copyright information

© SISSA 2013

Authors and Affiliations

  • Hiroyuki Fuji
    • 1
  • Sergei Gukov
    • 2
    • 3
  • Marko Stošić
    • 4
    • 5
  • Piotr Sulkowski
    • 2
    • 6
    • 7
  1. 1.Dept. of Physics, Graduate School of ScienceNagoya UniversityNagoyaJapan
  2. 2.California Institute of TechnologyPasadenaU.S.A.
  3. 3.Max-Planck-Institut für MathematikBonnGermany
  4. 4.Instituto de Sistemas e Robotica and CAMGSD, Instituto Superior TecnicoLisbonPortugal
  5. 5.Mathematical Institute SANUBeogradSerbia
  6. 6.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  7. 7.Faculty of PhysicsUniversity of WarsawWarsawPoland

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