Theory of holomorphic maps of two-dimensional complex manifolds to toric manifolds and type A multi-string theory

Abstract

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 $({\mathbb{C}}^{\ast }{)}^N$ 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 $N_{\mathrm{comp}}$ topological strings of type A. Here $N_{\mathrm{comp}}$ is the number of compactifying divisors of the toric target. Before the mirror transformation these strings are vortex (actually, holomortex) strings.

Cited by in corpus (1)

• Generalized cohomological field theories in the higher order formalism