Project Details
Projekt
Equivalence of D-brane categories
Applicant
Professor Dr. Duco van Straten
Subject Area
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Term
from 2000 to 2005
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 5252068
According to Strominger, Yau and Zaslow, mirror symmetry of Calabi-Yau manifolds should be understood in terms dual torus fibrations. On the other hand, Kontsevich proposed to formulate mirror symmetry as an equivalence of Ao-categories, one based on holomorphic D-branes and the other on special Lagrangian D-branes. These objects should be interchanged under T-duality (Fourier-Makai transform). Even for the simplest cases where the Calabi-Yau is a torus, many important questions remain nanswered. Although recently there has been progress in understanding the structure of SYZ-fibrations for certain explicit Calabi-Yau spaces, one is far from understanding the behaviour of the corresponding D-brane-categories. The purpose of the project is to find a general formulation for categorical mirror symmetry, encompassing, and to prove as much as possible for the simplest Calabi-Yau spaces like tori and quotients thereof.
DFG Programme
Priority Programmes
