  Superstring/M-theory compactified on compact Ricci flat manifolds have
recently been conjectured to exhibit instabilities whenever the metrics do not
have special holonomy. We use worldsheet conformal field theory to investigate
instabilities of Type II superstring theories on compact, Ricci flat, spin
3-manifolds including a worldsheet description of their spin structures. The
instabilities are signalled by the appearance of stringy tachyons at small
radius and a negative (1-loop) vacuum energy density at large radius. We
briefly discuss the extension to higher dimensions.
