# $z-$Weyl gravity in higher dimensions

## TL;DR

This paper explores a higher-dimensional gravity theory with anisotropic conformal invariance, leading to a 4D scalar-tensor effective theory, and discusses potential implications for the cosmological constant problem.

## Contribution

It introduces a novel anisotropic conformal gravity framework in higher dimensions with an adjustable parameter z, extending previous models and analyzing its 4D effective theory.

## Key findings

- The 4D effective action is a scalar-tensor theory coupled with a nonlinear sigma model.
- No classical restrictions on the anisotropy parameter z.
- Potential applications to the cosmological constant problem are proposed.

## Abstract

We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter $z$ which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of $z$ at the classical level and possible applications to the cosmological constant problem with a specific choice of $z$ is discussed.