Derived categories and GLSM phase transitions

In theoretical physics, a gauged linear sigma model (GLSM) is a supersymmetric gauge theory which admits multiple phases with different physical behaviors. Such theories have been described in mathematical terms by means of variations of GIT, often yielding pairs of non isomorphic but derived equivalent Calabi—Yau pairs. We provide a GLSM description for a pair (X, Y), where X is Fano and Y is of general type, and with an argument based on window categories and matrix factorization we construct an embedding of the derived category of Y in the derived category of X.

Joint work with Enrico Fatighenti, Michal Kapustka and Giovanni Mongardi.