Kink solutions in generalized 2D dilaton gravity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2023
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| _version_ | 1866911768596447232 |
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| author | Zhong, Yuan Guo, Heng Liu, Yu-Xiao |
| author_facet | Zhong, Yuan Guo, Heng Liu, Yu-Xiao |
| contents | 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 $\mathcal X= -\frac12 (\nabla φ)^2$, say $\mathcal F(\mathcal X)$, and the kink is generated by a canonical scalar matter field $ϕ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13786 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kink solutions in generalized 2D dilaton gravity Zhong, Yuan Guo, Heng Liu, Yu-Xiao High Energy Physics - Theory General Relativity and Quantum Cosmology 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 $\mathcal X= -\frac12 (\nabla φ)^2$, say $\mathcal F(\mathcal X)$, and the kink is generated by a canonical scalar matter field $ϕ$. 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. |
| title | Kink solutions in generalized 2D dilaton gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2308.13786 |