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We propose a gravitational response theory for point defects (hedgehogs)binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in4+1 dimensions, where the point defect is extended into a line, a coupling ofthe bulk defect texture with the gravitational field is introduced.Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current runningalong the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for thenon-Abelian nature of the zero modes in 3+1 dimensions. It is then shown toalso encode the angular momentum density which permeates throughout the bulkbetween hedgehog-anti-hedgehog pairs.

Effective response theory for zero energy Majorana bound states in three spatial dimensions