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| Autori principali: | , , , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2505.16108 |
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| _version_ | 1866915607978442752 |
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| author | Yu, Peng Zhong, Yuan Wang, Ziqi Wang, Hui Zhang, Mengyang |
| author_facet | Yu, Peng Zhong, Yuan Wang, Ziqi Wang, Hui Zhang, Mengyang |
| contents | In this work, we present two brane-world-type solutions in a two-dimensional (2D) dilaton gravity model with singular space-time backgrounds. By employing a first-order superpotential formalism, we first construct the 2D analogues of the thick brane solution previously given by Gremm and analyze the corresponding linear scalar perturbations. We show that for a model with canonical scalar matter fields, the effective potential of the linear perturbation equation is a singular Pöschl--Teller~II type, which does not admit bound states. However, for a model with non-canonical scalar fields, the effective potential becomes an exactly solvable Pöschl--Teller~I potential, which has an infinite tower of normalizable bound states. We also present a second analytic solution inspired by the work of Girardello \emph{et al.}, but with non-canonical scalar field. In this case, the linear perturbation equation is a Schrödinger equation with the Eckart potential, which is also exactly solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shape-invariant Potentials and Singular Spaces Yu, Peng Zhong, Yuan Wang, Ziqi Wang, Hui Zhang, Mengyang High Energy Physics - Theory General Relativity and Quantum Cosmology In this work, we present two brane-world-type solutions in a two-dimensional (2D) dilaton gravity model with singular space-time backgrounds. By employing a first-order superpotential formalism, we first construct the 2D analogues of the thick brane solution previously given by Gremm and analyze the corresponding linear scalar perturbations. We show that for a model with canonical scalar matter fields, the effective potential of the linear perturbation equation is a singular Pöschl--Teller~II type, which does not admit bound states. However, for a model with non-canonical scalar fields, the effective potential becomes an exactly solvable Pöschl--Teller~I potential, which has an infinite tower of normalizable bound states. We also present a second analytic solution inspired by the work of Girardello \emph{et al.}, but with non-canonical scalar field. In this case, the linear perturbation equation is a Schrödinger equation with the Eckart potential, which is also exactly solvable. |
| title | Shape-invariant Potentials and Singular Spaces |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.16108 |