If we assume that the swampland conjectures, etc. regarding de sitter vacuas existence in the string / F-theory landscape turn out to be incorrect (and therefore we can assume the problem is well-posed), would all such solutions have broken supersymmetry?
There are a number of obvious “difficulties” with formulating (at least for the case of generic qft on curved spacetime) particle theories on de Sitter like spaces (ex. non-trivial hamiltonian from vanishing of globally timelike killing vectors, etc.). One feature of de Sitter space, that is probably obvious but likely not trivial (at least from first glance) is the non-existence of positive conserved energy and its requirement for broken supersymmetry.
Have I made an error, or is this a “just so” theorem regarding de Sitter vacua and the necessity for broken supersymmetry?