3d analogs of Argyres-Douglas theories and knot homologies

Understand

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.