Mirror Manifolds And Topological Field Theory

TL;DR

This paper reviews how topological field theory and twisted N=2 sigma models can be used to understand mirror manifolds, focusing on the mirror map and its role in mirror symmetry.

Contribution

It provides a review of existing results on mirror manifolds through topological field theory, with new insights into the mirror map construction.

Findings

Insights into the mirror map from topological field theory

Connection between N=2 sigma models and mirror symmetry

Potential relevance to mirror moduli space construction

Abstract

These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.