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The geometrical underpinnings of a specific class of Dirac operators isdiscussed. It is demonstrated how this class of Dirac operators allow to relatevarious geometrical functionals like, for example, the Yang-Mills action andthe functional of non-linear $\sigma-$models (i.e. of (Dirac) harmonic maps).These functionals are shown to be similar to the Einstein-Hilbert action withcosmological constant (EHC). The EHC may thus be regarded as a "genericfunctional". As a byproduct, the geometrical setup presented also allows toavoid the issue of "fermion doubling" as usually encountered, for instance, inthe geometrical discussion of the Standard Model in terms of Dirac operators.Furthermore, it is demonstrated how the geometrical setup presented allows toderive the cosmological constant term of the EHC from the Einstein-Hilbertfunctional and the action of a purely gauge coupling Higgs field.

The Einstein-Hilbert action with cosmological constant as a functional of generic form