UV properties of Galileons: Spectral Densities

Understand

We propose a picture for the UV properties of Galileon field theories.

• We conjecture that Galileons, and all theories incorporating the Vainshtein mechanism, fall into Jaffe's class of `non-localizable' field theories characterized by an exponential growth in their Kallen-Lehmann spectral densities.
• Similar properties have been argued to arise for Little String Theories and M-theory.
• For such theories, the notion of micro-causality and the time ordering used to define the S-matrix and correlation functions must be modified, and we give a Lorentz invariant prescription for how this can be achieved.