Mirror Symmetry And Quantum Geometry
Kentaro Hori
TL;DR
This paper explores the application of mirror symmetry as T-duality in gauge systems to study quantum geometry with D-branes, demonstrating a method to realize mirror duality through wrapped D-branes and Floer theory.
Contribution
It introduces a novel approach to realize mirror duality using D-branes on torus fibers and Floer theory, extending the Strominger-Yau-Zaslow program.
Findings
Mirror symmetry can be derived from T-duality in gauge systems.
D-branes wrapped on torus fibers reproduce mirror duality.
Floer theory of intersecting Lagrangians is crucial for the analysis.
Abstract
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ D-branes wrapped on torus fibers to reproduce the mirror duality itself, realizing the program of Strominger-Yau-Zaslow in a slightly different context. Floer theory of intersecting Lagrangians plays an essential role.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models