T-structures on a local 4-Calabi-Yau variety

Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize a large class of t-structures in the relevant Calabi-Yau category and try to calculate the combinatorics of them.