Aspects of $(d+D)$-dimensional Anisotropic Conformal Gravity

TL;DR

This paper explores anisotropic conformal gravity in higher dimensions, proposing models that address hierarchy issues, suggest UV-complete quantum gravity, and connect to known theories like the CGHS model.

Contribution

It introduces a novel anisotropic conformal gravity framework in $(d+D)$ dimensions with spontaneous symmetry breaking and explores its implications for hierarchy problems and quantum gravity.

Findings

Proposes a resolution to the hierarchy problem in (4,1) models.

Suggests a UV-complete, unitary quantum gravity in (2,2) case.

Derives the CGHS model in a (2,1) setting.

Abstract

We discuss various aspects of anisotropic gravity in $(d+D)$-dimensional spacetime where $D$ dimensions are treated as extra dimensions. It is based on the foliation preserving diffeomorphism invariance and anisotropic conformal invariance. The anisotropy is embodied by introducing a factor $z$ which discriminates the scaling degree of the extra $D$ dimensions against the $d$-dimensional base spacetime and Weyl scalar field which mediates the anisotropic scaling symmetry. There is no intrinsic scale but a physical scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking. Some vacuum solutions are obtained and we discuss an issue of `size separation' between the base spacetime and the extra dimensions. The size separation means large hierarchy between the scales appearing in the base spacetime and the extra dimensions respectively. We also discuss interesting theories obtained from our model. In the case of (4,1), we propose a resolution of hierarchy problem and discuss comparison with the results of the brane-world model. In a $(d,D)=(2,2)$ case, we suggest a UV-complete unitary quantum gravity which might become Einstein gravity in IR. In a certain (2,1) case, we obtain CGHS-model.