Teleparallel conformal invariant models induced by Kaluza–Klein reduction

Abstract

We study the extensions of teleparallism in the Kaluza–Klein (KK) scenario by writing the analogous form to the torsion scalar in terms of the corresponding antisymmetric tensors, given by , in the four-dimensional new general relativity (NGR) with arbitrary coefficients a, b and c. After the KK dimensional reduction, the Lagrangian in the Einstein-frame can be realized by taking 2a + b + c = 0 with the ghost-free condition for the one-parameter family of teleparallelism. We demonstrate that the pure conformal invariant gravity models can be constructed by the requirements of 2a + b = 0 and c = 0. In particular, the torsion vector can be identified as the conformal gauge field, while the conformal gauge theory can be obtained by 2a + b + 4c = 0 or 2a + b = 0, which is described on the Weyl–Cartan geometry Y4 with the ghost-free conditions 2a + b + c > 0 and . We also consider the weak field approximation and discuss the non-minimal coupled term of the scalar current and torsion vector. For the conformal invariant models with 2a + b = 0, we find that only the anti-symmetric tensor field is allowed rather than the symmetric one.