MiS Preprint Repository

The geometrical underpinnings of a certain class of Dirac operators is discussed. It is demonstrated how these Dirac operators allow to relate various geometric functionals like, for example, the Yang-Mills and the functional of non-linear $\sigma -$models (i.e. (Dirac) harmonic maps). In fact, all these functionals are shown to be intimately related to the Einstein-Hilbert action with cosmological constant (EHC). Therefore, the latter may be regarded as a kind of "generic functional". In addition, the geometrical setup presented also allows to avoid the issue of the "fermion doubling".