Geometry of Multi-Flavor Galileon-Like Theories

TL;DR

This paper classifies a broad class of Lorentz-invariant scalar theories with Galileon-like symmetries using Lie algebra methods, revealing their structure and potential applications in cosmology and high-energy physics.

Contribution

It introduces a Lie-algebraic framework to systematically classify multi-flavor Galileon-like theories based on internal symmetry representations.

Findings

Infinite catalog of theories characterized by affine Lie algebra representations

Theories exhibit enhanced soft-limit scattering amplitude scaling

Framework applicable to cosmology and high-energy physics models

Abstract

We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of low-energy effective couplings, by specifying an affine representation of the Lie algebra of physical, non-redundant internal symmetries and an invariant metric on its target space. This creates an infinite catalog of theories relevant for both cosmology and high-energy physics thanks to their special properties such as enhanced scaling of scattering amplitudes in the soft limit.