Squares, Roots and the Einstein-Hilbert Functional

In contrast to the quadratic Yang-Mills action, Einstein's theory of gravity is based on a functional which is linear in the curvature. This is known to have far reaching consequences. Many attempts have been made over the last decades to recast Einstein's theory of gravity into a Yang-Mills like form. In the following we up-side-down this point of view and show how to express Yang-Mills gauge theories linearly in the curvature of Dirac bundles and thereby recast gauge theories into a "gravity like form". For this we discuss a canonical action functional within the geometrical setting of Dirac bundles in the light of a new global Lichnerowicz like formula.