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arXiv · 2308.13786

Kink solutions in generalized 2D dilaton gravity

Yuan Zhong·Heng Guo·Yu-Xiao Liu
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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.

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Yuan Zhong, Heng Guo, Yu-Xiao Liu. 2023-08-26. Kink solutions in generalized 2D dilaton gravity. https://doi.org/10.1016/j.physletb.2024.138471

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