# A higher-order Skyrme model

## TL;DR

This paper introduces a higher-order Skyrme model with derivative terms up to twelfth order, demonstrating improved stability properties over previous models but also revealing complex dynamical instabilities.

## Contribution

The authors construct a new higher-order Skyrme model with positive-definite static energies and analyze its stability, addressing issues found in earlier models.

## Key findings

- Static energies are positive definite, indicating stability against static perturbations.
- The model exhibits nonlinear dynamical instabilities, distinct from Ostrogradsky instability.
- At low energies, the Hamiltonian remains stable against time-dependent perturbations.

## Abstract

We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However, we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally, we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.