Obstacles for dS in Supersymmetric Theories

We present two types of obstacles for constructing de Sitter space in supersymmetric theories that appear as effective theories of quantum gravity. The first obstacle concerns de Sitter critical points in extended supergravity with charged massless gravitini. We show that all such critical points have a Hubble scale of the same order or above the UV cutoff dictated by the magnetic Weak Gravity Conjecture. The second obstacle concerns the dynamics of the goldstino in models with non-linearly realized supersymmetry, such as string models involving anti-branes. We show, using an exact renormalization group approach, that the goldstino sector has an instability toward the formation of condensates, which may have important qualitative consequences for de Sitter constructions involving anti-brane uplifts.