标题： 关于广义$SU(2)$Yang-Mills-Higgs 模型中依赖标量的耦合$θ$-项的BPS方程 显示英文标题

标题： On BPS Equations of Generalized $SU(2)$ Yang-Mills-Higgs Model with Scalars-Dependent Coupling $θ$-term

摘要： 我们考虑了一个最广义的$SU(2)$Yang-Mills-Higgs 模型，该模型由场的一阶导数的二次项组成，即广义的$SU(2)$Yang-Mills-Higgs 模型，并带有附加的与标量相关的耦合$\theta$项。利用BPS拉格朗日方法，通过采用最一般的BPS拉格朗日密度，尝试推导出BPS单极子和磁单极子的Bogomolnyi方程。我们得到了更为普遍的Bogomolnyi方程以及所有标量相关耦合之间的关系。从这些方程可以看出，存在一族参数化的BPS单极子解，该参数为实常数$\gamma$，而对于BPS磁单极子，还存在一个额外的参数，即$\theta$项的耦合。有趣的是，即使对于单一的BPS磁单极子，我们发现$\theta$项的耦合值仅对BPS磁单极子的电荷提供额外贡献，这与Witten在Phys.Lett.B 86 (1979)中的结果一致，从而可以确定我们得到的是BPS单极子还是BPS磁单极子。 显示英文摘要

摘要： We consider a most general $SU(2)$ Yang-Mills-Higgs model consist of terms up to quadratic in first-derivative of the fields, that is the generalized $SU(2)$ Yang-Mills-Higgs with additional scalars-dependent coupling $\theta$-term. Using the BPS Lagrangian method we try to find Bogomolnyi's equations for BPS monopoles and dyons by taking most general BPS Lagrangian density. We obtain more general Bogomolnyi's equations and a relation between all scalars dependent couplings. From these equations we can see there is a family of BPS monopole solutions parameterized by a real constant $\gamma$, while for BPS dyons there is an additional parameter which is the coupling of $\theta$-term. Interestingly even for a single BPS dyon we find the value of $\theta$-term's coupling only gives additional contribution to electric charge of BPS Dyons, which is in accordance with Witten's result in Phys.Lett.B 86 (1979), and thus can determine whether we get BPS monopoles or BPS dyons.