Authors: Fuji, Hiroyuki
Gukov, Sergei
Stošić, Marko 
Sulkowski, Piotr
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: 3d analogs of Argyres-Douglas theories and knot homologies
Journal: Journal of High Energy Physics
Volume: 2013
Issue: 1
Issue Date: 8-Feb-2013
Rank: M21
ISSN: 1029-8479
DOI: 10.1007/JHEP01(2013)175
We study singularities of algebraic curves associated with 3d 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 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.
Keywords: ChernSimons Theories | Differential and Algebraic Geometry | Duality in Gauge Field Theories | Supersymmetric gauge theory
Publisher: Springer Link
Project: Japan Society for the Promotion of Science, Grant no. 21740179

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