We argue that conformal invariance is a common thread linking scalar effective field theories appearing in the double copy. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories conformal invariance is a much more stringent constraint than scale invariance.

中文翻译：

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标量有效场论的隐藏共形不变性

我们认为，保形不变性是连接出现在双重副本中的标量有效场理论的共同线索。对于具有四次 ${\cal O}(p^4)$ 顶点的导数耦合标量，经典保形不变性规定了一个无限的附加相互作用塔，这些相互作用与 Dirac-Born-Infeld 理论完全一致，在解析上持续到时空维度 $D= 0 美元。对于四次 ${\cal O}(p^6)$ 顶点的情况，经典保形不变性将理论约束为 $D=-2$ 维度的特殊伽利略。我们还通过证明它们的振幅由共形 Ward 恒等式唯一地固定来验证这些理论的共形不变性。在这些理论中，保形不变性是比尺度不变性更严格的约束。