Non-birational twisted derived equivalences in abelian GLSMs

Understand

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions.

• Examples of gauged linear sigma models with non-birational Kahler phases are a relatively new phenomenon.
• Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation.
• We also propose a more general understanding of the relationship between Kahler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov's `homological projective duality.' Along the way, we shall see how `noncommutative spaces' (in Kontsevich's sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories.