论文标题
$ t^2/\ mathbb {z} _n $ orbifolds上的索引定理
Index theorem on $T^2/\mathbb{Z}_N$ orbifolds
论文作者
论文摘要
我们在$ t^2/\ mathbb {z} _n $ orbifolds上调查了固定点的手性零模式和绕点数。研究表明，手性零模式的Atiyah-Singer索引定理导致$ n _+-n _- =（ - v _ ++ v _-）/2n $，其中$ n _ {\ pm} $是$ \ pm $ \ pm $ pm $ chiral $ v _ pm}的数量是$ t^2/\ mathbb {z} _n $。此公式与我们的零模式计数公式互补，该公式在具有非零通量背景$ m \ neq 0 $的磁化孔上，一致地替换为计数公式$ n_+ -n_-- =（2m-v_++++ v _--）/2n $。
We investigate chiral zero modes and winding numbers at fixed points on $T^2/\mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, 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 $T^2/\mathbb{Z}_N$. This formula is complementary to our zero-mode counting formula on the magnetized orbifolds with non-zero flux background $M \neq 0$, consistently with substituting $M = 0$ for the counting formula $n_+ - n_- = (2M - V_+ + V_-)/2N$.
