Two-dimensional (bi-)scalar gravities from four-dimensional Horndeski

TL;DR

This paper derives a two-dimensional bi-scalar gravity model from four-dimensional Horndeski theory using Kaluza-Klein reduction, introducing a concise formulation and analyzing perturbations to identify healthy modes.

Contribution

It presents a novel two-dimensional bi-scalar gravity framework from four-dimensional Horndeski theory, including a new identity and perturbation analysis for healthy modes.

Findings

Support for a single healthy propagating mode.

A concise bi-scalar Lagrangian formulation.

Mapping between 2D dilaton gravity and 4D Horndeski theory.

Abstract

We develop a classical two-dimensional bi-scalar gravity based on the Kaluza-Klein reduction applied to the four-dimensional Horndeski theory. One of the scalar fields arises from the original four-dimensional theory, while the extra scalar emerges from the reduction process. We also introduce a two-dimensional bi-scalar identity that allows for a more concise and elegant reformulation of the resulting bi-scalar Lagrangian. Additionally, we study the linear perturbations around a static background to demonstrate that the bi-scalar theory may support a single healthy propagating mode. Furthermore, by restricting the scalar fields, we investigate a general single scalar theory that is identical to the two-dimensional Horndeski theory up to a boundary term. Our results provide a framework to map a generic two-dimensional dilaton gravity into four-dimensional Horndeski theory.