  We analytically derive a compatible family of effective field theories that
uniquely describe topological superconductors in 3D, their 2D boundary and
their 1D defect lines. We start by deriving the topological field theory of a
3D topological superconductor in class DIII, which is consistent with its
symmetries. Then we identify the effective theory of a 2D topological
superconductor in class D living on the gapped boundary of the 3D system. By
employing the holographic correspondence we derive the effective chiral
conformal field theory that describes the gapless modes living on the defect
lines or effective boundary of the class D topological superconductor. We
demonstrate that the chiral central charge is given in terms of the 3D winding
number of the bulk which by its turn is equal to the Chern number of its gapped
boundary.
