Multi-Galileons, solitons, and Derrick’s theorem

Galileon models, which were developed in the context of modified gravity, give a class of Lagrangians containing derivative interactions without introducing higher order derivatives in the equations of motion. Here we extend the analysis to an arbitrary number of scalars, and examine the restrictions imposed by an internal symmetry, focusing in particular on SU(N) and SO(N). This therefore extends the possible gradient terms that may be included when constructing topological objects such as sigma model lumps.

Figure 1

Static solitonic solutions for winding number $n=1$ (solid-blue line) and $n=2$ (dashed-red line). The spherically symmetric ansatz (48) is used. The energies of them are $E^{(1)}\simeq 101.8$ and $E^{(2)}\simeq 462.3$ respectively.