论文标题
$ t^2/\ mathbb {z} _n $ orbifolds带有磁性通量的索引和绕组数字
Index and winding numbers on $T^2/\mathbb{Z}_N$ orbifolds with magnetic flux
论文作者
论文摘要
我们分析了$ t^2/{\ mathbb {z}} _ n $（$ n = 2,3,4,6 $）Orbifolds带有磁性通量的独立手性零模式的数量和固定点处的绕点数。在$ n = 2 $的情况下，我们得出索引公式$ n _ {+} - n _ { - } = m/2+（ - v _ {+}+v _ { - }）/4 = m/2-v _ {+}+}/2+使用trace公式，$ n $ v _ {\ pm} $是$ t^2/{\ mathbb {z}} _ 2 $上固定点处的绕点数的总和。我们还获得了公式$ n _ {+} - n _ { - } = m/n+（ - v _ {+}+v _ { - }）/（2n）/（2n）= m/n-v _ {+}/n+1 $ for $ n = 3,4,6 $在假设下$ n = 3,4,6 $。
We analyze the number of independent chiral zero modes and the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$) orbifolds with magnetic flux. In the case of $N=2$, we derive the index formula $n_{+}-n_{-}=M/2+(-V_{+}+V_{-})/4=M/2-V_{+}/2+1$ by using the trace formula, where $n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$ are the sums of the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_2$. We also obtain the formula $n_{+}-n_{-}=M/N+(-V_{+}+V_{-})/(2N)=M/N-V_{+}/N+1$ for $N=3,4,6$ under an assumption.
