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.
In this work we consider the higher dimensional Skyrme model, with spatial dimension $d > 3$, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, \(B\geq 1\), a modified generalized hedgehog ansatz is used where we assign an integer \(n_i\) for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-inva…
A curious correspondence has been known between Landau models and non-linear sigma models: Reinterpreting the base-manifolds of Landau models as field-manifolds, the Landau models are transformed to non-linear sigma models with same global and local symmetries. With the idea of the dimensional hierarchy of higher dimensional Landau models, we exploit this correspondence to present a systematic procedure for construction of non-linear sigma models in higher dimensions. We explicitly derive $O(2k+1)$ non-linear sigma models in $2k$ dimension based on the parent tensor gauge theories that origina…
We construct hairy static black holes of higher dimensional general coupling Einstein-Skyrme theories with the scalar potential turned on and the cosmological constant is non-positive in which the scalar multiplets satisfy $O(d+1)$ model constraint where $d$ is the spatial dimension of the spacetime and $d \ge 3$. Some physical properties of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region are discussed. Then, we prove that these black hole solutions exist globally which may have finite energy for non-positive cosmological constant. Finally, we use p…
In this paper we construct a class of hairy static black holes of higher dimensional Einstein-Skyrme theories with the cosmological constant $Λ\le 0$ whose scalar is an $SU(2)$ valued field. The spacetime is set to be conformal to $ \mathcal{M}^4 \times \mathcal{N}^{N-4}$ where $\mathcal{M}^4$ and $\mathcal{N}^{N-4}$ are a four dimensional spacetime and a compact Einstein $(N-4)$-dimensional submanifold for $N \ge 5$, respectively, whereas $N=4$ is the trivial case. We discuss the behavior of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region. Then, we…
Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model
Compact Q-balls and Q-shells within a $CP^N$ Skyrme-Faddeev type model
Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）；Universidade de São Paulo（圣保罗大学）；Jagiellonian University（雅盖隆大学）；Tokyo University of Science（东京科学大学）；National Institute of Technology, Toyota College（国立丰田工学院）
An omega-meson extension of the Skyrme model - without the Skyrme term but including the pion mass - first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained energy minimisation problem within a natural geometric framework and studied analytically on compact domains, and numerically on Euclidean space. Using a constrained second-order Newton flow algorithm, classical energy minimisers are constructed for various values of the omega-pion coupling. At high coupling, these Skyrmion solutions are qualitatively similar …
To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a meson. Each instanton generates a unique skyrmion and we reinterpret the $8N$ instanton moduli as physical degrees of freedom in the Skyrme model. In this p…
Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes
The Assam Royal Global University（阿萨姆皇家全球大学）；Al-Hussein Bin Talal University（侯赛因·本·塔拉勒大学）；Eastern Mediterranean University（东地中海大学）
We formulate four-dimensional $\mathcal{N} = 1$ supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski's ghosts, as gauged linear sigma models. We then study Bogomol'nyi-Prasad-Sommerfield equations preserving 1/2 or 1/4 supersymmetries. We find that there are distinct branches, that we call canonical ($F=0$) and non-canonical ($F\neq 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the ${\mathbb C}P^N$ model, we obtain a supersymmetric ${\mathbb C}P^N$…
