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We consider the interplay of disorder and interactions upon the gaplesssurface states of 3D topological superconductors. The combination of topologyand superconducting order inverts the action of time-reversal symmetry, so thatextrinsic time-reversal invariant surface perturbations appear only as"pseudomagnetic" fields (abelian and non-abelian vector potentials, whichcouple to spin and valley currents). The main effect of disorder is to inducemultifractal scaling in surface state wavefunctions. These criticallydelocalized, yet strongly inhomogeneous states renormalize interaction matrixelements relative to the clean system. We compute the enhancement orsuppression of interaction scaling dimensions due to the disorder exactly,using conformal field theory. We determine the conditions under whichinteractions remain irrelevant in the presence of disorder for symmetry classesAIII and DIII. In the limit of large topological winding numbers (many surfacevalleys), we show that the effective field theory takes the form of aFinkel'stein non-linear sigma model, augmented by theWess-Zumino-Novikov-Witten term. The sigma model incorporates interactioneffects to all orders, and provides a framework for a controlled perturbativeexpansion; the inverse spin or thermal conductance is the small parameter. Forclass DIII we show that interactions are always irrelevant, while in class AIIIthere is a finite window of stability, controlled by the disorder. Outside ofthis window we identify new interaction-stabilized fixed points.

Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors