Derrick's theorem beyond a potential

TL;DR

This paper investigates the existence of stable solitonic solutions in galileon and related derivatively coupled theories, concluding that such stable solitons do not exist in these classes of models.

Contribution

It demonstrates the absence of stable solitons in galileon theories and related derivatively coupled models, extending Derrick's theorem beyond potential-based theories.

Findings

Galileon theories lack stable solitonic solutions.

No stable solitons in derivatively coupled theories like superfluids and k-essence.

Results extend Derrick's theorem to broader classes of theories.

Abstract

Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.