Locally Weyl invariant massless bosonic and fermionic spin-1/2 action in the $\bf (W_{n(4)},g)$ and $\bf (U_{4},g)$ space-times

TL;DR

This paper develops locally Weyl invariant actions for massless bosons and fermions in four-dimensional non-metric and torsional space-times, extending conformal gravity theories to include non-metricity and contortion effects.

Contribution

It introduces new Weyl invariant actions for bosonic and fermionic fields in non-metric and torsional geometries, broadening the scope of conformal gravity models.

Findings

Invariant actions are constructed in Weyl $(W_n, g)$ and Riemann-Cartan $(U_4, g)$ space-times.

Additional contributions to conformal gravity are calculated.

Results apply to a subgroup of Weyl-Cartan $(Y_4, g)$) space-time.

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.