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

TL;DR

This paper constructs new non-geometric Bridgeland stability conditions on wrapped Fukaya categories, demonstrating that stable objects under these conditions admit special Lagrangian representatives, thus advancing understanding in higher-dimensional mirror symmetry.

Contribution

It introduces the first higher-dimensional examples of stability conditions away from the large complex structure limit where stable implies special Lagrangian.

Findings

Stable objects admit special Lagrangian representatives.

Construction of non-geometric stability conditions using mirror symmetry.

First such examples beyond the large complex structure limit.

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.