A Hidden Symmetry of the Galileon

TL;DR

The paper identifies a hidden extended shift symmetry for galileon theories at a special parameter choice, showing invariance under a quadratic shift in spacetime coordinates and a quadratic in the field. This symmetry enforces a form where only even powers of the field appear (up to a rescaling of the energy scale) and, combined with galileon duality, yields a unique, parameter-fixed theory. The extended symmetry enlarges the algebra with a new S_{\mu\nu} generator and implies a soft-phi theorem that explains the observed $\mathcal{O}(q^3)$ soft limit for quartic galileons, aligning with recent results and suggesting broader generalizations to higher shifts. These results illuminate why certain galileon-like theories exhibit enhanced soft behavior and have implications for their UV structure and S-matrix properties.

Abstract

We show that there is a special choice of parameters for which the galileon theory is invariant under an enhanced shift symmetry whose non-linear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one with only even powers of the field, with no free coefficients, and accounts for the improved soft limit behavior observed in the quartic galileon S-matrix.