Multi-galileons, solitons and Derrick's theorem

TL;DR

This paper extends the analysis of multi-scalar Galileon theories with internal symmetries like SU(N) and SO(N), exploring their implications for stabilizing topological solitons and generalizing previous single-scalar results.

Contribution

It introduces a framework for multi-scalar Galileon theories with internal symmetries, expanding the types of gradient terms available for stabilizing solitonic solutions.

Findings

Extended Galileon theories to multiple scalars with SU(N) and SO(N) symmetries.

Identified new gradient terms that can stabilize topological solitons.

Provided conditions for second-order equations of motion in multi-scalar models.

Abstract

The field theory Galilean symmetry, which was introduced in the context of modified gravity, gives a neat way to construct Lorentz-covariant theories of a scalar field, such that the equations of motion contain at most second-order derivatives. Here we extend the analysis to an arbitrary number of scalars, and examine the restrictions imposed by an internal symmetry, focussing in particular on SU(N) and SO(N). This therefore extends the possible gradient terms that may be used to stabilise topological objects such as sigma model lumps.