论文标题
零模式计数公式和Orbifold压缩中的零
Zero-mode counting formula and zeros in orbifold compactifications
论文作者
论文摘要
我们彻底分析了带有磁性磁通背景的独立零模式的数量及其在环形Orbifold $ t^2/\ mathbb {z} _n $（$ n = 2、3、4、6 $）上的零点，其灵感来自Atiyah-Singer Index theorem。我们首先显示属于$ \ mathbb {z} _ {n} $ eigenvalue $η$的Orbifold零模式的数字$n_η$的完整列表。由于事实证明，$n_η$非常复杂，这取决于flux Quanta $ m $，Scherk-Schwarz twist opeas $（α_1，α_2）$和$ \ Mathbb {z} _ {n} _ {n} $ eigenvalue $η$，似乎很难在$n_η$中被清楚地解释。但是，我们成功地找到了单个零模式计数公式$n_η=（m-v_η）/n + 1 $，其中$v_η$表示Orbifold $ t^2/\ mathbb {z z} _n $的固定点上的绕组数的总和。该公式显示为任何模式。
We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold $T^2/\mathbb{Z}_N$ ($N = 2, 3, 4, 6$) with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the number $n_η$ of orbifold zero modes belonging to $\mathbb{Z}_{N}$ eigenvalue $η$. Since it turns out that $n_η$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $(α_1, α_2)$, and the $\mathbb{Z}_{N}$ eigenvalue $η$, it seems hard that $n_η$ can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula $n_η = (M-V_η)/N + 1$, where $V_η$ denotes the sum of winding numbers at the fixed points on the orbifold $T^2/\mathbb{Z}_N$. The formula is shown to hold for any pattern.
