  We discuss a phenomenon in supersymmetric field theory and string theory
whereby compactifying one of the dimensions of spacetime on an arbitrarily
large circle can cause BPS states to become unstable. We exemplify this by
considering 5d N=1 theories on a circle and their embeddings into M-theory via
geometric engineering. This implicates a subtle relationship between the BPS
states of M-theory on a Calabi-Yau threefold, X, and those of type IIA on X
with an arbitrary value of the coupling constant. Intuition for this phenomenon
is provided by considering F-theory on a complex K3 surface in a limit where it
degenerates to a real K3 surface.
