论文标题
$ s^2 $和$ s^5 $的Orbifolds中的相对规模分离
Relative scale separation in orbifolds of $S^2$ and $S^5$
论文作者
论文摘要
在包含$ S^Q/γ$因子的Orbifold Vacua中，我们计算了比例分离的相对顺序，$ r $，定义为$ s^q $的标量laplacian的最低laplaciant的特征值的比率，归于$ s^q $。对于$ q = 2 $和$γ$的有限亚组为$（3）$，或$ q = 5 $和$γ$ $ su（3）$的有限亚组，可以实现的最大比例相对顺序为$ r = 21 $或$ r = 12 $。对于光滑的$ s^5 $ orbifolds，最大相对尺度分离为$ r = 4.2 $。不变理论的方法在构建$γ$ invariant球形谐波方面非常有效，并且可以很容易地将其推广到其他Orbifolds。
In orbifold vacua containing an $S^q/Γ$ factor, we compute the relative order of scale separation, $r$, defined as the ratio of the eigenvalue of the lowest-lying $Γ$-invariant state of the scalar Laplacian on $S^q$, to the eigenvalue of the lowest-lying state. For $q=2$ and $Γ$ finite subgroup of $SO(3)$, or $q=5$ and $Γ$ finite subgroup of $SU(3)$, the maximal relative order of scale separation that can be achieved is $r=21$ or $r=12$, respectively. For smooth $S^5$ orbifolds, the maximal relative scale separation is $r=4.2$. Methods from invariant theory are very efficient in constructing $Γ$-invariant spherical harmonics, and can be readily generalized to other orbifolds.
