Locally Weyl invariant massless bosonic and fermionic spin-1/2 action in the $({\mathbf{W}}_{\mathbf{n}(4)},\mathbf{g})$ and $({\mathbf{U}}_4,\mathbf{g})$ space-times

Abstract

We search for a real bosonic and fermionic action in four dimensions which both remain invariant under local Weyl transformations in the presence of non-metricity and contortion tensor. In the presence of the non-metricity tensor the investigation is extended to Weyl $(W_n,g)$ space-time while when the torsion is encountered we are restricted to the Riemann-Cartan $(U_4,g)$ space-time. Our results hold for a subgroup of the Weyl-Cartan $(Y_4,g)$ space-time and we also calculate extra contributions to the conformal gravity.

16 pages

References in corpus (1)

• Torsion action and its possible observables

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