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arXiv · 2406.17388

Two-dimensional (bi-)scalar gravities from four-dimensional Horndeski

M. Shams Nejati·M. H. Vahidinia
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Abstract

We develop a classical two-dimensional bi-scalar gravity based on the Kaluza-Klein reduction applied to the four-dimensional Horndeski theory. One of the scalar fields arises from the original four-dimensional theory, while the extra scalar emerges from the reduction process. We also introduce a two-dimensional bi-scalar identity that allows for a more concise and elegant reformulation of the resulting bi-scalar Lagrangian. Additionally, we study the linear perturbations around a static background to demonstrate that the bi-scalar theory may support a single healthy propagating mode. Furthermore, by restricting the scalar fields, we investigate a general single scalar theory that is identical to the two-dimensional Horndeski theory up to a boundary term. Our results provide a framework to map a generic two-dimensional dilaton gravity into four-dimensional Horndeski theory.

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M. Shams Nejati, M. H. Vahidinia. 2024-06-25. Two-dimensional (bi-)scalar gravities from four-dimensional Horndeski. https://doi.org/10.1088/1361-6382%2Fad85be

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