We provide a complete classification of Poincar\'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,\phi)$ theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly.

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对称标量

我们提供了 Poincar\'e 不变标量场理论的完整分类，其中包含一组扩大的经典对称性以导数导数，即所谓的 $P(X,\phi)$ 理论，在两个或多个时空方面。我们只发现了三种可能性：Dirac-Born-Infeld、Cuscuton 和 Scaling 理论。后两类动作涉及标量场的任意函数。作为一个应用，我们使用标度对称性来推导出对低能有效场理论的威尔逊系数的无限约束集。此外，我们研究将这些结果扩展到宇宙学（FLRW）和（反）德西特时空。我们特别发现 Cuscuton 动作在任何具有杀死矢量场的背景时空周围都有一组通用的对称性，