3d analogs of Argyres-Douglas theories and knot homologies

Abstract

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 Poincare 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.

40 pages, 14 figures

References in corpus (9)

• Floer homology and knot complements
• Exploring Curved Superspace
• Generalized Superconformal Index for Three Dimensional Field Theories
• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Super-A-polynomial for knots and BPS states
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
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Cited by in corpus (38)

• Holomorphic Blocks in Three Dimensions
• Fivebranes and 3-manifold homology
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• Colored HOMFLY polynomials for the pretzel knots and links
• Knots-quivers correspondence
• Resurgence in complex Chern-Simons theory
• BPS states, knots and quivers
• On colored HOMFLY polynomials for twist knots
• Knot polynomials in the first non-symmetric representation
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Sequencing BPS Spectra
• Colored Kauffman Homology and Super-A-polynomials
• 3d-3d Correspondence Revisited
• On genus expansion of superpolynomials
• Reformulated invariants for non-torus knots and links
• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• Link polynomial calculus and the AENV conjecture
• Differential expansion and rectangular HOMFLY for the figure eight knot
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories
• Factorization of differential expansion for antiparallel double-braid knots
• Equivariant Verlinde formula from fivebranes and vortices
• BPS counting for knots and combinatorics on words
• Cabling procedure for the colored HOMFLY polynomials
• Branches, quivers, and ideals for knot complements
• Lectures on Knot Homology and Quantum Curves
• On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\bar{S}$ for representation $R=[3,1]$ with multiplicities
• On possible existence of HOMFLY polynomials for virtual knots
• More on Homological Supersymmetric Quantum Mechanics
• Colored HOMFLY polynomials from Chern-Simons theory
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Super-A-polynomial
• Musings on SVD and pseudo entanglement entropies
• Knot Complement, ADO-Invariants and their Deformations for Torus Knots
• Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
• The colored Jones polynomials as vortex partition functions
• Permutohedra for knots and quivers
• On ambiguity in knot polynomials for virtual knots