A unified gauge and gravity theory with only matter fields

We propose a purely fermionic action with gauge and general relativistic invariances. This implies a unified treatment of gravity and gauge theories without elementary metric tensor and gauge boson fields. At the quantum level this scale-invariant theory generates, as vacuum properties, both a metric and a scale Λ which becomes related to the Planck mass. The analysis of the spectrum displays, besides the original fermions, massless composite vierbein and gauge bosons, as well as a set of states with masses of order Λ. In a low-energy regime in which these heavy modes are not excited, the light sector is shown to be governed by a phenomenological action which coincides with the conventional gravity-gauge-matter theory without cosmological term and with a Newton constant and gauge couplings determined by Λ. For increasing energies, the gauge interactions are predicted to grow towards their merging with gra Λ, the theory differs substantially from the conventional one, not even allowing a definition of a space-time metric and providing hints for a milder ultraviolet behaviour.