  We consider the interplay of disorder and interactions upon the gapless
surface states of 3D topological superconductors. The combination of topology
and superconducting order inverts the action of time-reversal symmetry, so that
extrinsic time-reversal invariant surface perturbations appear only as
"pseudomagnetic" fields (abelian and non-abelian vector potentials, which
couple to spin and valley currents). The main effect of disorder is to induce
multifractal scaling in surface state wavefunctions. These critically
delocalized, yet strongly inhomogeneous states renormalize interaction matrix
elements relative to the clean system. We compute the enhancement or
suppression of interaction scaling dimensions due to the disorder exactly,
using conformal field theory. We determine the conditions under which
interactions remain irrelevant in the presence of disorder for symmetry classes
AIII and DIII. In the limit of large topological winding numbers (many surface
valleys), we show that the effective field theory takes the form of a
Finkel'stein non-linear sigma model, augmented by the
Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction
effects to all orders, and provides a framework for a controlled perturbative
expansion; the inverse spin or thermal conductance is the small parameter. For
class DIII we show that interactions are always irrelevant, while in class AIII
there is a finite window of stability, controlled by the disorder. Outside of
this window we identify new interaction-stabilized fixed points.
