  I provide two solutions to the problem of categorifying quantum link
invariants, which work uniformly for all gauge groups and originate in geometry
and string theory. The first is based on a category of equivariant B-type
branes on ${\cal X}$ which is a moduli space of singular $G$-monopoles on
${\mathbb R}^3$. In this paper, I give the second approach, which is based on a
category of equivariant A-type branes on $Y$ with potential $W$. The first and
the second approaches are related by equivariant homological mirror symmetry:
$Y$ is homological mirror to $X$, a core locus of ${\cal X}$ preserved by an
equivariant action related to $\mathfrak{q}$. The theory of equivariant
A-branes on $Y$ is the same as the derived category of modules of an algebra
$A$, which is a cousin of the algebra considered by Khovanov, Lauda, Rouquier
and Webster, but simpler. The result is a new, geometric formulation of
Khovanov homology, which generalizes to all groups. In part III, I will explain
the string theory origin of the two approaches, and the relation to an approach
being developed by Witten. The three parts may be read independently.
