Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

We prove a general criterion which ensures that fractional Calabi--Yau category of dimension $\leq 2$ admits unique Serre-invariant stability condition, up to the action universal cover $\text{GL}^+_2(\mathbb{R})$. apply this result Kuznetsov component $\text{Ku}(X)$ cubic threefold $X$. In particular, we show all known conditions on are invariant with respect Serre functor and thus lie in same orbit As an application, moduli space Ulrich bundles rank $\geq $X$ is irreducible, answering question asked by Lahoz, Macr\`i Stellari.