Discreteness of silting objects and t-structures in triangulated categories

We introduce the notion of ST-pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a finite-dimensional algebra. For an ST-pair $(\text{C},\text{D})$, we construct an order-preserving map from silting objects in $\text{C}$ to bounded $t$-structures on $\text{D}$ and show that the map is bijective if and only if $\text{C}$ is silting-discrete if and only if $\text{D}$ is $t$-discrete. Based on a work of Qiu and Woolf, the above result is applied to show that if $\text{C}$ is silting-discrete then the stability space of $\text{D}$ is contractible. This is used to obtain the contractibility of the stability spaces of some Calabi–Yau triangulated categories associated to Dynkin quivers.