论文标题
广义$ su（2）$ yang-mills-higgs型号中是否有BPS dyon？
Are There BPS Dyons in The Generalized $SU(2)$ Yang-Mills-Higgs Model?
论文作者
论文摘要
我们在$ su（2）$ su（2）$ yang-mills-higgs模型中使用众所周知的Bogomolny方程，用于BPS单子和dyon，以在BPS Lagrangian方法下获得BPS Lagrangian密度的显式形式。然后，我们将此BPS lagrangian密度概括，并使用它来得出几个可能的广义Bogomolny方程，并在广义$ su（2）$ yang-mills-higgs模型中使用（OUT）其他约束方程。我们还计算了广义模型的应力 - 能量量张量，并认为如果应力张量密度的所有组件在BPS限制中为零，则BPS单极和Dyon溶液是稳定的。这种稳定性要求意味着标量依赖性耦合是通过方程相互关联的，这与〜\ cite {atmaja：2018-cod}获得的耦合不同，然后选择特定的广义bogomolny's方程，而没有其他约束方程，而没有其他约束方程。我们表明〜\ cite {atmaja：2018代码}中的计算实际上是不完整的。 Under the Julia-Zee ansatz, the generalized Bogomolny's equations imply all scalar fields-dependent couplings must be constants, whose solutions are the BPS dyons of the $SU(2)$ Yang-Mills-Higgs model~\cite{Prasad:1975kr}, or in another words there are no generalized BPS dyon solutions under the Julia-Zee ansatz.我们提出了两种可能的方法来获得广义BPS dyon，其中至少一个依赖性耦合的标量磁场不是恒定的，即使用不同的ANSATZE，例如轴向对称的ANSATZ用于更高的拓扑电荷dyons；和/或通过考虑最通用的BPS Lagrangian密度。
We use the well-known Bogomolny's equations, in general coordinate system, for BPS monopoles and dyons in the $SU(2)$ Yang-Mills-Higgs model to obtain an explicit form of BPS Lagrangian density under the BPS Lagrangian method. We then generalize this BPS Lagrangian density and use it to derive several possible generalized Bogomolny's equations, with(out) additional constraint equations, for BPS monopoles and dyons in the generalized $SU(2)$ Yang-Mills-Higgs model. We also compute the stress-energy-momentum tensor of the generalized model, and argue that the BPS monopole and dyon solutions are stable if all components of the stress-tensor density are zero in the BPS limit. This stability requirement implies the scalar fields-dependent couplings to be related to each other by an equation, which is different from the one obtained in~\cite{Atmaja:2018cod}, and then picks particular generalized Bogomolny's equations, with no additional constraint equation, out of those possible equations. We show that the computations in~\cite{Atmaja:2018cod} are actually incomplete. Under the Julia-Zee ansatz, the generalized Bogomolny's equations imply all scalar fields-dependent couplings must be constants, whose solutions are the BPS dyons of the $SU(2)$ Yang-Mills-Higgs model~\cite{Prasad:1975kr}, or in another words there are no generalized BPS dyon solutions under the Julia-Zee ansatz. We propose two possible ways for obtaining generalized BPS dyons, where at least one of the scalar fields-dependent couplings is not constant, that are by using different ansatze, such as axially symmetric ansatz for higher topological charge dyons; and/or by considering the most general BPS Lagrangian density.
