Kink solutions in generalized 2D dilaton gravity

TL;DR

This paper investigates static kink solutions in a generalized 2D dilaton gravity model with a scalar matter field, revealing a first-order formalism, Schrödinger-like perturbation equations, and exact solutions including a sine-Gordon type kink with solvable perturbations.

Contribution

It introduces a generalized kinetic term for the dilaton, derives a simple first-order formalism, and finds exact kink solutions with solvable perturbations in 2D dilaton gravity.

Findings

First-order formalism for arbitrary kinetic functions

Schrödinger-like linear perturbation equations

Exact sine-Gordon type kink solutions with solvable perturbations

Abstract

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one $\mathcal X= -\frac12 (\nabla \varphi)^2$, say $\mathcal F(\mathcal X)$, and the kink is generated by a canonical scalar matter field $\phi$. It is found that for arbitrary $\mathcal F(\mathcal X)$, the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schr\"odinger-like equation with factorizable Hamiltonian operator. After choosing appropriate $\mathcal F(\mathcal X)$ and superpotential, we obtain a sine-Gordon type kink solution with pure AdS$_2$ metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.