# Generalized 2D dilaton gravity and KGB

## TL;DR

This paper demonstrates that nonminimal scalar-curvature coupling in 2D dilaton gravity can be reformulated as kinetic gravity braiding, aligning with 2D Horndeski theory, and finds static solutions with linearly time-dependent scalar fields.

## Contribution

It explicitly shows the equivalence between nonminimal coupling in 2D dilaton gravity and KGB, and derives static solutions with dynamic scalar configurations.

## Key findings

- Recasting of nonminimal coupling as KGB in 2D
- Explicit static solutions with linearly time-dependent scalar fields
- Alignment of 2D dilaton gravity with Horndeski theory

## Abstract

We show explicitly that the nonminimal coupling between the scalar field and the Ricci scalar in 2D dilaton gravity can be recast in the form of kinetic gravity braiding (KGB). This is as it should be, because KGB is the 2D version of the Horndeski theory. We also determine all the static solutions with a linearly time-dependent scalar configuration in the shift-symmetric KGB theories in 2D.