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.

中文翻译：

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来自四维 Horndeski 的二维（双）标量引力


我们基于应用于四维 Horndeski 理论的 Kaluza-Klein 约简开发了一种经典的二维双标量引力。其中一个标量场来自原始的四维理论，而额外的标量则来自归约过程。我们还引入了一个二维双标量恒等式，它允许对生成的双标量拉格朗日进行更简洁和优雅的重新表述。此外，我们研究了静态背景周围的线性扰动，以证明双标量理论可能支持单一的健康传播模式。此外，通过限制标量场，我们研究了一个通用的单标量理论，该理论与二维 Horndeski 理论相同，直到边界项。我们的结果提供了一个框架，将通用的二维膨胀子引力映射到四维 Horndeski 理论。