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arXiv · 2111.06836

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

Olga Chekeres·Andrey S. Losev·Pavel Mnev·Donald R. Youmans
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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 $(\mathbb{C}^*)^N$ 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.

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Olga Chekeres, Andrey S. Losev, Pavel Mnev, Donald R. Youmans. 2021-11-12. Theory of holomorphic maps of two-dimensional complex manifolds to toric manifolds and type A multi-string theory. https://doi.org/10.1134/s0021364022010027

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