Spontaneous symmetry breaking in 5D conformally invariant gravity

TL;DR

This paper investigates spontaneous symmetry breaking in a 5D conformally invariant gravity model, demonstrating exact solutions that lead to 4D Minkowski space and symmetry breaking, with stability analysis revealing a conformal quantum mechanics description.

Contribution

It introduces a novel 5D conformally invariant gravity model with exact solutions for symmetry breaking and analyzes its stability and potential applications.

Findings

Exact 4D Minkowski vacuum solution found

Spontaneous conformal symmetry breaking demonstrated

Stability analysis reveals conformal quantum mechanics description

Abstract

We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implement the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting system is described by the conformal quantum mechanics. Possible applications to the spontaneous symmetry breaking of time-translational symmetry along the dynamical fifth direction and the brane-world scenario are discussed.