  For certain terms in the action, supersymmetry can forbid an infinite number
of possible contributions. We study whether such protection can occur in
quantum gravity even without sufficient supersymmetry. We focus on whether the
superpotential can vanish exactly in four-dimensional N=1 theories, and if the
prepotential can be exactly cubic in N=2 theories. We investigate these
questions in string theory and find that for almost all known string
constructions the corrections allowed by supersymmetry do occur. However, we do
find some special settings where all the corrections can be proven to vanish.
These examples all share the common feature that they are related, through a
certain orbifolding by a discrete gauged R-symmetry element, to a higher
supersymmetric theory. Motivated by these results, we propose a Swampland
criterion that any theory which enjoys such protection beyond its realised
supersymmetry must have a direct connection to a higher supersymmetric theory.
