Fractional Calabi-Yau categories via Landau-Ginzburg models

We give criteria for the existence of a Serre functor on the derived category of a gauged Landau–Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi–Yau subcategory of a gauged Landau–Ginzburg model and a geometric context for crepant categorical resolutions. We explicitly describe our framework in the toric setting. As a consequence, we generalize several theorems and examples of Orlov and Kuznetsov, ending with new examples of semi-orthogonal decompositions containing (fractional) Calabi–Yau categories.