  We discuss a (2+1) dimensional topological superconductor with $N_f$ left-
and right-moving Majorana edge modes and a $\mathbb{Z}_2\times \mathbb{Z}_2$
symmetry. In the absence of interactions, these phases are distinguished by an
integral topological invariant $N_f$. With interactions, the edge state in the
case $N_f=8$ is unstable against interactions, and a $\mathbb{Z}_2\times
\mathbb{Z}_2$ invariant mass gap can be generated dynamically. We show that
this phenomenon is closely related to the modular invariance of type II
superstring theory. More generally, we show that the global gravitational
anomaly of the non-chiral Majorana edge states is the physical manifestation of
the bulk topological superconductors classified by $\mathbb{Z}_8$.
