Stability Conditions and Algebraic Hearts for Acyclic Quivers

Abstract: We study stability conditions on the derived category of a finite connected acyclic quiver. We prove that, for any stability condition on the derived category, its heart can be obtained from an algebraic heart by a rotation of phases. Consequently, we establish the connectedness of the space of stability conditions. Furthermore, we prove that every stability condition $\sigma$ admits a full $\sigma$-exceptional collection.