From the perspective of topological string, holomorphic curves in a Calabi-Yau 3-fold ending on a Lagrangian deforms the Chern-Simons theory on the Lagrangian. Mathematically this can be interpreted as open Gromov-Witten invariants with values in the skein module of the Lagrangian. We discuss this definition and show how it combined with a specific deformation of the complex structure known as...
We consider one complex structure parameter mirror families $W$ of Calabi-Yau 3-folds with Picard-Fuchs equations of hypergeometric type. By mirror symmetry the even D-brane masses of the orginal Calabi-Yau $M$ can be identified with four periods w.r.t. to an integral symplectic basis of $H_3(W,Z)$ at the point of maximal unipotent monodromy. It was discovered by Chad Schoen in 1986 that...
11. Lessons from six dimensions for geometry, the string landscape/swampland, and the nature of matter
The geometrical formulation of string theory through "F-theory" provides a nonperturbative framework that connects geometry with the physics of gauge theories and matter fields coupled to supergravity. In six dimensions, this has led to new insights into the global structure of the "landscape" of supergravity theories and string theory vacua, has provided new mathematical results on Calabi-Yau...