Topological Mirrors and Quantum Rings

TL;DR

This paper explores duality and mirror symmetry in string theory, highlighting the role of loop spaces and reformulating mirror symmetry as an equivalence between topological theories, with suggestions for broader generalizations.

Contribution

It introduces a simplified reformulation of mirror symmetry as an equivalence between topological sigma models and Landau-Ginzburg models, emphasizing the role of loop spaces.

Findings

Mirror symmetry can be expressed as an equivalence of topological theories.

Loop spaces are crucial for understanding the geometrical origin of dualities.

Proposals for generalizing mirror symmetry are discussed.

Abstract

Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: Topological sigma models and topological Landau-Ginzburg models. Some suggestions are made for generalization of the notion of mirror symmetry.