The special Galileon stands out amongst scalar field theories due to its soft limits, non-linear symmetries and scattering amplitudes. This prompts the question what the origin of its underlying symmetry is. We show that it is intimately connected to general relativity: the special Galileon is the Goldstone mode of the affine group, consisting of linear coordinate transformations, analogous to the dilaton for conformal symmetries. We construct the corresponding metric, and discuss various relations to gravity, Yang-Mills and the non-linear sigma-model.

中文翻译：

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作为微分同胚的戈德斯通的特殊伽利略

由于其软限制、非线性对称性和散射幅度，特殊的伽利略在标量场理论中脱颖而出。这就提出了一个问题，它的潜在对称性的起源是什么。我们证明它与广义相对论密切相关：特殊伽利略是仿射群的戈德斯通模式，由线性坐标变换组成，类似于共形对称的膨胀。我们构建了相应的度量，并讨论了与重力、杨米尔斯和非线性西格玛模型的各种关系。