Kink solutions in generalized 2D dilaton gravity

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 $\mathcal{X}=-\frac{1}{2}(\nabla \phi {)}^2$, say $\mathcal{F}(\mathcal{X})$, and the kink is generated by a canonical scalar matter field $\varphi$. 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 Schrödinger-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.

7 pages, 2 figures