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3d analogs of Argyres-Douglas theories and knot homologies

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 T K labeled by knots, whose partition functions package Poincaré polynomials of the S r -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 T K 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 S r-colored HOMFLY homologies.

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Correspondence to Hiroyuki Fuji.

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ArXiv ePrint: 1209.1416

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Fuji, H., Gukov, S., Stošić, M. et al. 3d analogs of Argyres-Douglas theories and knot homologies. J. High Energ. Phys. 2013, 175 (2013). https://doi.org/10.1007/JHEP01(2013)175

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Keywords

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