Teleparallel Conformal Invariant Models induced by Kaluza-Klein Reduction

Chao-Qiang Geng; Ling-Wei Luo

doi:10.1088/1361-6382/aa6ca1

paper

Teleparallel Conformal Invariant Models induced by Kaluza-Klein Reduction

arXiv:1612.00166 · doi:10.1088/1361-6382/aa6ca1

Abstract

We study the extensions of teleparallism in the Kaluza-Klein (KK) scenario by writing the analogous form to the torsion scalar $T_{NGR}$ in terms of the corresponding antisymmetric tensors, given by $T_{NGR} = a T_{ij k} T^{ij k} + b T_{ij k} T^{k j i} + c T^{j}_{j i} T^{k}_{k}^{i}$ , 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 $2 a + b + c = 0$ with the ghost-free condition $c \leq 0$ for the one-parameter family of teleparallelism. We demonstrate that the pure conformal invariant gravity models can be constructed by the requirements of $2 a + b = 0$ 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 $2 a + b + 4 c = 0$ or $2 a + b = 0$ , which is described on the Weyl-Cartan geometry $Y_{4}$ with the ghost-free conditions $2 a + b + c > 0$ and $c \neq = 0$ . 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 $2 a + b = 0$ , we find that only the anti-symmetric tensor field is allowed rather than the symmetric one.

23 pages, 1 figure, revised version accepted by Classical and Quantum Gravity

Teleparallel Conformal Invariant Models induced by Kaluza-Klein Reduction

Abstract

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