Special Lagrangians and Bridgeland stable objects beyond geometric stability conditions: the product case

Abstract

We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical K\"unneth formulae. These stability conditions correspond to certain holomorphic volume forms, under which we prove that every stable object admits a special Lagrangian representative. This provides the first higher-dimensional examples of stability conditions away from the large complex structure limit for which ``stable implies special Lagrangian" is proved.