I’ll describe some new examples where the derived category of one variety can be embedded inside the derived category of a second variety. These examples are all given by a single construction, and they include the quintic 3-fold sitting in a certain Fano 11-fold, and a new derived equivalence between two Calabi-Yau 5-folds. We also recover the `Pfaffian-Grassmannian’ derived equivalence between two non-birational Calabi-Yau 3-folds.
The proof is inspired by string theory, and uses a non-abelian gauged linear sigma model to relate both derived categories to some categories of (global) matrix factorizations. This is joint work with Richard Thomas.