论文标题
Abelian测量$ \ MATHBB {CP}^2 $ -Sigma模型的两种半本地宇宙字符串与重力耦合
Two species of semi-local cosmic strings in Abelian gauged $\mathbb{CP}^2$-sigma models coupled to gravity
论文作者
论文摘要
我们研究了一个半本地的Abelian Higgs Sigma模型，该模型具有$ \ mathbb {cp}^2 $ - 值的标量字段与重力结合。我们在此系统中建立了自偶性所需的条件，并在$ \ mathbb {cp}^2 $的参考图中获得宇宙字符串，无论是自dual字符还是从自偶数点出发。在最低地图集的其他两个图表中，过渡函数将全局$ su（2）$对称性打破到Abelian子组$ e^{iσ^3α} $。在这种情况下，使用过渡功能可以构建新的自偶联结构，从而定义了第二种宇宙字符串。由于存在标量场的势能，每个物种都在目标空间的不同界面区域中采用值，并且最自然地使用$ \ mathbb {cp}^2 $的特定图表来描述。
We study a semi-local Abelian Higgs sigma model with $\mathbb{CP}^2$-valued scalar fields coupled to gravity. We establish the conditions needed for self-duality in this system and obtain cosmic strings, both of self-dual character and out of the self-dual point, in the reference chart of $\mathbb{CP}^2$. In any of the other two charts of a minimum atlas, the transition functions break the global $SU(2)$ symmetry to the Abelian subgroup $e^{i σ^3 α}$. In this context, using the transition functions a new self-dual structure can be constructed, which defines a second species of cosmic strings. Because of the presence of a potential energy for the scalar fields, each species takes values in a different bounded region of the target space and is most naturally described using a particular chart of $\mathbb{CP}^2$.
