Theodora Ioannidou, Arpad Lukacs
An extended version of the BPS Skyrme model that admits time-dependent solutions is discussed. Initially, by introducing a power law at the original potential term of the BPS Skyrme model the existence, stability and structure of the corresponding solutions is investigated. Then, the frequencies and half-lifes of the radial oscillations of the constructed time-dependent solutions are determined.
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In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny's equations and their corresponding energies with topological charge $B>0$ is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term pro…
Exact BPS bound for noncommutative baby Skyrmions
非对易婴儿Skyrme模型是二维西格玛模型的Moyal变形加上Skyrme项，具有群值或格拉斯曼目标。在这个模型中，精确的阿贝尔孤子解已被确定分析，奇异的交换极限。在任何给定的格拉斯曼，我们建立一个BPS的能量泛函，这是饱和的婴儿Skyrmions。这就断言了它们对于单位电荷的稳定性，正如我们在二阶微扰理论中所测试的那样。
We show that a suitable background field can bring a non-BPS topological soliton into its BPS, self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background.
We propose and investigate several complex versions of extensions and restrictions of the Skyrme model with a well-defined Bogomolny-Prasad-Sommerfield (BPS) limit. The models studied possess complex kink, anti-kink, semi-kink, massless and purely imaginary compacton BPS solutions that all have real energies. The reality of the energies for a particular solution is guaranteed when a modified antilinear CPT-symmetry maps the Hamiltonian functional to its parity time-reversed complex conjugate and the solution field to itself or a new field with degenerate energy. In addition to the known BPS Sk…
Topological duality between vortices and planar skyrmions in BPS theories with APD symmetries
BPS baby Skyrme模型是baby Skyrme模型的子模型，其中非线性西格玛模型项被抑制。它们的skyrmion解决方案饱和的BPS界，相应的静态能量功能下保持面积的同态（APD）是不变的。本文证明了BPS baby Skyrme模型中带有非平凡拓扑荷$Q_{b} \in π_2(S^2)$（一个缠绕数）的孤子与带有拓扑荷$Q_{v}\in π_1(S^1)$（一个涡旋数）的BPS涡旋模型中的涡旋是对偶的，即两个模型的BPS解之间存在一个映射.两个模型的BPS解的相应能量密度相同。对偶性的进一步结果是，对偶BPS涡旋模型继承了BPS性质和BPS婴儿Skyrme模型的无限多对称性（APD）。最后，我们证明了相同的拓扑对偶继续保持U（1）规范版本的模型。
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…
Magnetothermodynamics of BPS baby skyrmions
研究了零温下BPS baby Skyrme模型描述的Skyrmion型物质的磁热力学。我们证明了该模型的BPS属性也保持对应于一个渐近恒定的磁场的边界条件。得到了BPS束缚和相应的饱和束缚的BPS方程，并进一步证明了通过重新定义超势可以在规范模型中引入压力。有趣的是，这与所谓的假超对称方法中的非极值型解有关。最后，我们计算了在外加恒定磁场$H$和外加压力$P$作用下的磁化BSP baby Skyrmions的状态方程，即，$V=V(P,H)$，其中$V$是由skyrmions占据的“体积”（面积）。我们表明，BPS婴儿skyrmions形成一个铁磁介质。
We study the BPS Skyrme model with potentials breaking the isospin symmetry and analyse how properties of exact solitonic solutions depend on a form of the isospin breaking potential. In the case of the strong symmetry breaking a new topologic structure is observed which enables us to decompose a BPS skyrmion into a lower dimensional defect localised on a brane (kink). We investigate some thermodynamical properties of such solitons as well as the role of the symmetry breaking potential in the resulting mean-field equation of state.
The vector BPS Skyrme model
我们分析了（3+1）维BPS Skyrme模型的矢量介子公式，其中的第六次幂项的原始的，可积的BPS Skyrme模型（拓扑或重子流平方）的一阶导数特性被替换为矢量介子$ω_μ$和重子流之间的耦合。我们发现，该模型仍然是可积的广义可积性和几乎可解的（可约为一组两个一阶常微分方程）的重子电荷的任何值的意义。进一步，我们分析了两个单参数单真空势族：旧Skyrme势和所谓的BPS势的拓扑孤子的出现。根据参数的值，我们发现几个定性不同的可能性。在无质量的情况下，我们有一个参数区域没有skyrmion，一个独特的紧凑skyrmion与不连续的一阶导数在边界（相当于，与源项位于边界，屏幕的拓扑电荷），和库仑局域孤子。对于大质量矢量介子，除了非skyrmion区域和唯一的C紧孤子外，我们还发现了指数和幂次局域skyrmion。此外，我们发现（对于特定的潜在）BPS解决方案，即，饱和Bogomolny束缚（无质量和有质量矢量介子）的skyrmions，对于重子电荷的较高值是不稳定的。最后，该模型的性质进行了比较，它的婴儿版本在（2+1）维，并与原来的BPS Skyrme模型，有助于更好地理解后者。
The BPS Skyrme model has many exact analytic solutions in flat space. We generalize the model to a curved space or spacetime and find that the solutions can only be BPS for a constant time-time component of the metric tensor. We find exact solutions on the curved spaces: a 3-sphere and a 3-hyperboloid; and we further find an analytic gravitating Skyrmion on the 3-sphere. For the case of a nontrivial time-time component of the metric, we suggest a potential for which we find analytic solutions on anti-de Sitter and de Sitter spacetimes in the limit of no gravitational backreaction. We take the …
We consider the Skyrme model in the near-BPS limit. The BPS part is made of the sextic term plus a potential and the deformation is made of the standard massive Skyrme model controlled by a small parameter $ε\ll1$. In order to keep the perturbation under theoretical and computational control, we find a model for which BPS Skyrmions have compact support, henceforth denoted as compactons, and the spherically symmetric $B=1$ Skyrmion represents the most stable solution. We use the $ε$-expansion scheme to systematically calculate the corrections to the energy and compare with the exact numerical c…
We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate des…
A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of $2π$, which allows, in principle, to define thi…
We show that the minimally gauged BPS baby Skyrme model remains a BPS theory after coupling with gravity that is the topologically nontrivial configurations called baby Skyrmions carrying magnetic flux are solutions to a zero pressure equation. Following that the proper mass, magnetic flux and the proper geometric volume are linear function of the topological charge, while the total ADM mass and geometric radius get a contribution due to the gravitational interaction which is quadratic in the topological charge. All these quantities are found exactly as target space integrals (averages) of the…
We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient $ε$ as well as the standard pion mass term, with coefficient $εm_1^2$. The pions remain lighter than the soliton for any $ε$ and therefore the model is physically acceptable, even in the $ε\to 0$ limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations…
Near-BPS Skyrmions: Non-shell configurations and Coulomb effects
核中相对较小的结合能表明它们可以很好地由近BPS Skyrmions表示，因为它们的质量大致与重子数$A.$成正比。为此，我们提出了一个推广的Skyrme模型，其项在π介子场的导数中达到六阶，并将非线性项$σ$和Skyrme项作为小扰动处理。对于我们的特殊选择的质量项（或潜在的）$V$，我们得到良好的行为分析的BPS型的解决方案与非壳结构的重子密度，而不是更复杂的壳状配置中发现的大多数扩展的Skyrme模型。随着静态和（等）转动能量，我们添加到核的质量往往被忽视的库仑能量和同位旋破缺项。拟合四个模型参数，我们发现每个核子的结合能$B/A$与实验数据的显着协议。这些结果支持了核可能是近BPS Skyrmions的观点。
Motivated by a class of near BPS Skyrme models introduced by Adam, Sánchez-Guillén and Wereszczyński, the following variant of the harmonic map problem is introduced: a map $ϕ:(M,g)\rightarrow (N,h)$ between Riemannian manifolds is restricted harmonic (RH) if it locally extremizes $E_2$ on its $SDiff(M)$ orbit, where $SDiff(M)$ denotes the group of volume preserving diffeomorphisms of $(M,g)$, and $E_2$ denotes the Dirichlet energy. It is conjectured that near BPS skyrmions tend to RH maps in the BPS limit. It is shown that $ϕ$ is RH if and only if $ϕ^*h$ has exact divergence, and a linear sta…
Skyrmions, instantons and holography
不久前，Atiyah和Manton观察到，计算杨-米尔斯瞬子的完整性可以很好地近似Skyrme模型的静态Skyrmion解。本文提供了一个扩展和解释这一结果，通过证明瞬子holonomies产生的BPS Skyrme模型，其中Skyrme场耦合到一个塔的矢量介子的精确解。忽略任何（或实际上所有）矢量介子会破坏尺度不变性，并消除Skyrmions的BPS性质。然而，它表明，截断的BPS Skyrme理论，其中只包括第一矢量介子，已经移动的Skyrme模型显着接近BPS系统。需要一个接近BPS系统的理论来再现原子核结合能的实验数据。在截断BPS理论中对Skyrmion进行了零模量子化，并将结果与核子的物理性质进行了比较。这种方法在五维闵可夫斯基时空中类似于酒井和杉本最近全息构建的Skyrme模型，该模型基于弯曲五维时空中杨-米尔斯-陈-西蒙斯理论的弦论推导。
A discrete analogue of the extended Bogomolny-Prasad-Sommerfeld (BPS) Skyrme model that admits time-dependent solutions is presented. Using the spacing h of adjacent lattice nodes as a parameter, we identify the spatial profile of the solution and the continuation of the relevant branch of solutions over the lattice spacing for different values of the potential (free) parameter α. In particular, we explore the dynamics and stability of the obtained solutions, finding that, while they generally seem to be prone to instabilities, for suitable values of the lattice spacing and for sufficiently la…
We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient $ε$. Classical solutions of this model, to leading order in $ε$, are called restricted harmonic maps. In the BPS limit ($ε\to 0$) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for…
Skyrmions in a truncated BPS theory
最近的研究表明，（4 + 1）维Yang-Mills理论可以写成一个（3 + 1）维BPS Skyrme模型，其中Skyrme场耦合到一个无限大的矢量介子塔上。将这座塔截断为一个单一的矢量介子，得到了标准Skyrme模型的扩展，即π介子与ρ介子耦合的理论，其中显著的简化是没有引入额外的自由参数。本文讨论这种截断理论，并给出了重子数为1~4的Skyrmions的结果。该方法涉及到使用的Atiyah-Manton建设，其中Skyrme场近似的杨米尔斯瞬子的holonomy的扩展版本。结果发现，耦合到ρ介子显着降低Skyrmion结合能，产生一个改进的比较与核的实验数据。一个截断，包括一个矢量和一个轴矢量介子也进行了研究，提供了一个模型的π介子，ρ介子和α 1介子。结合能因包含这个额外的介子而进一步降低，使Skyrmion能量更接近原子核的能量。通过将重子4号Skyrmion的能量等同于He-4的质量来固定能量单位，得到的所有较低重子数的质量都在实验值的20 MeV以内，这是一个比标准Skyrme模型小四倍的误差。
Noncommutative field theory description of quantum Hall skyrmions
我们利用非对易场论重新研究了没有塞曼分裂能的量子霍尔系统。我们分析了填充因子$ν=1$附近δ函数相互作用的BPS条件。多skyrmions饱和的BPS边界。$k$ skyrmions的模空间的维数是$4k+2$。通过推导有效的非线性$σ$模型拉格朗日量，证明了非对易场描述的优越性。
The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy-momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the "liquid droplet" model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin-isospin quantization, Coulomb energy, proton-neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the …
We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density - their thermodynamical functions as well as the equation of state agree in this limit. This f…
We consider the dielectric Skyrme model proposed recently, with and without the addition of the standard pion mass term. Then we write down Bogomol'nyi-type energy bounds for both the massless and massive cases. We further show that, except for when taking the strict BPS limit, the Skyrmions are made of 3 orthogonal dipoles that can always be placed in their attractive channel and form bound states. Finally, we study the model numerically and discover that, long before realistic binding energies are reached, the Skyrmions become bound states of well-separated point-particle-like Skyrmions. By …
Electroweak form factors of large nuclei as BPS skyrmions
本研究以BPS Skyrme模型为有效模型，计算重核的电弱形状因子，结果与实验数据吻合，为中微子精确实验提供了可靠方法。
Noncommutative Baby Skyrmions
我们的婴儿Skyrme模型的Moyal变形，酉或格拉斯曼的目标空间和没有潜在的长期。在阿贝尔情形下，普通非对易西格玛模型的径向BPS组态也解了婴儿Skyrme运动方程。这给出了一类精确解析的非对易婴儿Skyrmions，它们具有奇异的交换极限，但由于非对易性而对标度稳定。我们计算了它们的能量，研究了它们的稳定性，并确定了两个Skyrmion相互作用的渐近性质。
We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a ferromagnetic liquid. Such a transition can be generated by increasing the external pressure $P$ or by turning on an external magnetic field $H$. As a consequence, the topological phase where gauged BPS baby skyrmions exist, is a higher density phase. For smaller densities, obtained for smaller values of $P$ and $H$, a phase without solitons is reached. We find the critical line in the $P,H$ parameter space…
Symmetries and exact solutions of the BPS Skyrme model
BPS Skyrme模型是Skyrme型场论的一个特殊子类，它既有BPS束缚，又有无限多个孤子解（Skyrmions）饱和该束缚，这一特性使该模型成为研究核和强子某些性质的非常方便的一级近似。一个相关的性质，存在一个大群的对称变换，允许相当一般形状的解决方案，其中一些将是相关的物理核的描述。我们在这里研究的经典对称性的BPS Skyrme模型，应用它们来构造孤子解与某些规定的形状，构成了可靠的应用程序的模型的强相互作用物理的进一步重要的一步。
Lifshitz field theories with SDiff symmetries
我们考虑Lifshitz场论，其动力学临界指数z等于空间d的维数，并具有一大群基空间对称性，具体地说，是具有单位行列式的空间坐标变换（“特殊同态”）。所考虑的理论的场配置可能具有skyrmion、涡旋或单极的拓扑结构，尽管我们将详细的研究集中在skyrmion上。由此产生的Lifshitz场论有一个BPS的限制和精确的孤子解饱和的限制，以及时间相关的拓扑Q球解决方案。最后，我们研究了耦合到陈-西蒙斯规范场的Lifshitz场论的U（1）规范版本，其中BPS界和饱和该界的孤立子解继续存在。
Rotational-vibrational coupling in the BPS Skyrme model of baryons
在BPS Skyrme模型中计算了重子数为1的Hedgehog Skyrmion的转动-振动谱。核子和德尔塔罗珀共振的激发能略高于它们的实验值。再加上标准Skyrme模型中的这些激发能明显低于实验值，这就有力地证明了BPS Skyrme模型对重子和原子核物理性质的定量描述是必要的.
We consider a class of generalizations of the Skyrme model to five spacetime dimensions ($d=5$), which is defined in terms of an $O(5)$ sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps (Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions (Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the…
A BPS Skyrme model
在一组广义Skyrme模型中，我们确定了一个子模型，它既有无限多的对称性和Bogomolny界是饱和的无限多个精确孤子解。具体地说，子模型只包含重子流的平方和一个势项。此外，已经在经典水平上，该BPS Skyrme模型再现了原子核的液滴模型的某些特征。在这里，我们回顾模型的性质，我们讨论最简单的Skyrmion（核子）的半经典量子化。
On BPS Equations of Generalized $SU(2)$ Yang-Mills-Higgs Model with Scalars-Dependent Coupling $θ$-term
本研究通过 BPS 拉格朗日量方法，为含标量依赖耦合 $θ$ 项的广义 $SU(2)$ Yang-Mills-Higgs 模型推导出更一般的 Bogomolnyi 方程，揭示 BPS 磁单极子解由参数 $γ$ 刻画，而 $θ$ 项耦合仅影响双子电荷，与 Witten 结果一致。
Rational Maps, Monopoles and Skyrmions
我们讨论了BPS单极和Skyrmions之间的相似之处，并指出一个潜在的连接在黎曼领域之间的合理映射。这涉及到为Skyrme油田引入一种新的分析方法。我们用它来构建良好的近似几个已知的Skyrmions，包括所有的最小能量配置重子数9，和一些新的解决方案，如重子数17 Skyrme场的截断二十面体结构的巴基球。新的方法也被用来理解低的振动模式的Skyrmions，这是量子化所需的。一路上，我们发现了一个有趣的莫尔斯函数的空间的合理的地图，这可能是有用的理解森形式的模空间。
One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of the BPS Skyrme model at zero temperature and calculate its equation of state. Among other results, we find that classically (i.e. without taking into account quantum corrections) the compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero compression modulus. This suggests that the inclusion of the BPS submodel into the Skyrme model lagrangian may significantly reduce this too…
A baby--Skyrme model with anisotropic DM interaction: Compact skyrmions revisited
本文研究带DMI和势项的baby--Skyrme模型，其能量泛函源自费米子行列式的热核展开，包含拓扑荷Q=1的斯格明子及紧致子解，并探讨指数局域化DMI的影响。
Two recently found coupled BPS submodels of the Skyrme model are further analyzed. Firstly, we provide a geometrical formulation of the submodels in terms of the eigenvalues of the strain tensor. Secondly, we study their thermodynamical properties and show that the mean-field equations of state coincide at high pressure and read $p=\barρ/3$. We also provide evidence that matter described by the first BPS submodel has some similarity with a Bose-Einstein condensate. Moreover, we show that extending the second submodel to a non-BPS model by including certain additional terms of the full Skyrme m…
A BPS Skyrme model and baryons at large Nc
在具有Skyrme模型场内容的场论中，可以找到一个只包含重子流平方和势项的子模型。对于这个子模型，存在一个Bogomolny界，静态孤子解饱和这个界。此外，已经在经典水平上，该BPS Skyrme模型再现了原子核的液滴模型的某些特征。在这里，我们调查的模型更详细，此外，我们执行最简单的Skyrmion（核子）的刚性转子量子化。此外，我们还讨论了在大量色数N_c的限制下，该模型作为QCD的低能有效场论的可行性进一步提高的迹象。
We consider a restricted baby Skyrme-Maxwell scenario enlarged via the inclusion of a nontrivial magnetic permeability. We then proceed with the minimization of its total energy by means of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription, from which we get that the self-dual potential now depends on the magnetic permeability itself. As a result, we obtain not only the lower bound for the energy, but also the self-dual equations whose solutions saturate that bound. In such a context, we focus our attention on those time-independent gauged skyrmions with radial symmetry and no electric cha…
In this review, we summarise the main features of the BPS Skyrme model which provides a physically well-motivated idealisation of atomic nuclei and nuclear matter: 1) it leads to zero binding energies for classical solitons (while realistic binding energies emerge owing to the semiclassical corrections, the Coulomb interaction and isospin breaking); 2) it describes a perfect non-barotropic fluid already at the microscopic (field theoretical) level which allows to study thermodynamics beyond the mean-field limit. These properties allow for an approximate but analytical calculation of binding en…
We study several deformations of the Skyrme model in three dimensions with self-dual sectors of arbitrary baryonic charge. We show that, for a family of background metrics as well as for a family of field dependent couplings, the model has one BPS sector, which may have any topological charge. We also study the gravitating case, where there are infinite BPS sectors, provided that a cosmological constant is added to the model.
Nonlinear rigid-body quantization of Skyrmions
本文研究了Skyrme模型推广及高阶模型中Skyrmion的刚体量子化，发现标准Skyrme模型极限给出最小自旋能量贡献，并建立了Pottinger-Rathske模型及高阶模型的拓扑能量下界。
The Skyrme model and its generalisations provide a conceptually appealing field-theory basis for the description of nuclear matter and, after its coupling to gravity, also of neutron stars. In particular, a specific Skyrme submodel, the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model, allows both for an exact field-theoretic and a mean-field treatment of neutron stars, as a consequence of its perfect fluid property. A pure BPS Skyrme model description of neutron stars, however, only describes the neutron star core, by construction. Here we consider different possibilities to extrap…
Time-dependent and Non-BPS Solutions in N=6 Superconformal Chern-Simons Theory
研究了三维N=6超共形Chern-Simons理论与U（N）\times U（N）双基本物质场耦合的一类经典解.特别地，讨论了模糊球在无质量和有质量两种情况下的时间演化。对于有质量的情况，根据质量的值，存在具有不同行为的各种解。除了时间依赖的解决方案，我们分析了非BPS静态解决方案，代表平行M5/M5或M5/反M5膜悬挂多个M2膜。这些解类似于微扰弦论中连接两个平行（反）DP膜的基本弦。简要讨论了由已知BPS解的Lorentz boost得到的运动M5膜和等速畴壁解。
Exact analytic solutions of the Skyrme model defined on a spherically symmetric $R^{(1,1)} \times S^2$ geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the comp…
Multi-soliton dynamics in the Skyrme model
我们展示了在Skyrme模型中的多孤子的动力学散射的配置与电荷二，三，四。首先，我们从一个简单的轮廓函数和产品的Anantaly构造最大吸引配置。然后，使用一个复杂的数值算法，最初分离的skyrmions在近似对称的配置显示通过已知的最小能量配置散射。这些散射事件说明了许多相似之处，BPS的配置相同的电荷。一个简单的修改动力学的耗散制度，使我们能够计算的最小能量skyrmions的重子数为1至4的百分之几。
Non-BPS D-brane Near NS5-branes
利用快子场论有效作用量研究了非BPS Dp膜在k个NS 5膜附近的传播动力学.对于依赖于时间的快子凝聚，我们将集中讨论大快子的情况和非BPS D-膜接近NS 5-膜的情况。对于空间相关的快子凝聚，我们认为问题归结为研究k个NS 5-膜附近的D（p-1）-膜和D（p-1）-反膜的运动。
A class of BPS time-dependent 3-charge microstates from spectral flow
我们构造了一个无穷族的渐近平坦的3-荷解，其中含有D1，D5和动量荷。一般地，解也带有两个角动量。几何形状描述了D1-D5 CFT的所有基态的光谱流。这个族由四个函数参数化，这四个函数描述了一条封闭曲线在R^4中的嵌入和一个整数n，它标记了左扇区上的谱流。在给出任意基态谱流的一般公式后，我们给出了一个具体的构造例子。我们确定的渐近费用的解决方案，并显示与相应的CFT结果的匹配。
Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS$_4$
通过研究AdS$_4$中静态双曲BPS黑洞的单圈对数修正，发现经典吸引子平坦方向导致熵修正依赖于视界模量，并产生有效量子势动态稳定模量。
The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity is considered. We show that in an asymptotically flat space-time the model still possesses the BPS property, i.e., admits a BPS reduction to first order Bogomolnyi equations, which guarantees that the corresponding proper energy is a linear function of the topological charge. We also find the mass-radius relation as well as the maximal mass and radius. All these results are obtained in an analytical manner, which implies the complete solvability of this selfgravitating matter system. If a cosmological constant is adde…
We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number (or topological charge) $B=\pm 1$ but not for higher $|B|$. This implies that higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model. We provide a simple and explicit example for this possibility. Further, we s…
We construct static and also time-dependent solutions in a non-linear sigma model with target space being the flag manifold $F_2=SU(3)/U(1)^2$ on the four dimensional Minkowski space-time by analytically solving the second order Euler-Lagrange equation. We show the static solutions saturate an energy lower bound and can be derived from coupled first order equations though they are saddle point solutions. We also discuss basic properties of the time-dependent solutions.
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