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We investigate an index theorem for a Bogoliubov-de Gennes Hamiltonian (BdGH)describing a topological superconductor with Yang-Mills-Higgs couplings inarbitrary dimensions. We find that the index of the BdGH is determined solelyby the asymptotic behavior of the Higgs fields and is independent of the gaugefields. It can be nonvanishing if the dimensionality of the order parameterspace is equal to the spatial dimensions. In the presence of point defectsthere appear localized zero energy states at the defects. Consistency of theindex with the existence of zero energy bound states is examined explicitly ina vortex background in two dimensions and in a monopole background in threedimensions.

Generalized index theorem for topological superconductors with Yang-Mills-Higgs couplings