The Special Galileon as Goldstone of Diffeomorphisms

Understand

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.