We study
the field theory localizing to holomorphic
maps from a complex manifold of complex
dimension 2 to a toric target (a
generalization of A model). Fields are
realized as maps to (C∗)N where one includes special
observables supported on (1,1)-dimensional
submanifolds to produce maps to the toric
compactification. We study the mirror of
this model. It turns out to be a free theory
interacting with Ncomp topological strings of type A. Here
Ncomp is the number of compactifying
divisors of the toric target. Before the
mirror transformation these strings are
vortex (actually, holomortex) strings.