论文标题
$ t^2/\ mathbb {z} _n $的磁化爆炸歧管索引定理
Index theorem on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
论文作者
论文摘要
我们研究了$ t^2/{\ mathbb {z}} _ n \，（n = 2,3,4,6）$ orbifolds的爆炸歧管，带有磁性通量$ m $。由于爆炸的歧管没有奇异性，因此我们可以将Atiyah-Singer索引定理应用于它们。然后，我们建立零模式计数公式$ n _ {+} - n _ { - } =（m-v _ {+}）/n+1 $，其中$ v _ {+} $表示绕线数的总和，在$ t^2/{\ mathbb {z} _ n $ oins at at at at of points固定点上Orbifolds，并阐明公式的物理和几何含义。
We investigate blow-up manifolds of $T^2/{\mathbb{Z}}_N\,(N=2,3,4,6)$ orbifolds with magnetic flux $M$. Since the blow-up manifolds have no singularities, we can apply the Atiyah-Singer index theorem to them. Then, we establish the zero-mode counting formula $n_{+}-n_{-}=(M-V_{+})/N+1$, where $V_{+}$ denotes the sum of winding numbers at fixed points on the $T^2/{\mathbb{Z}}_N$ orbifolds, as the Atiyah-Singer index theorem on the orbifolds, and clarify physical and geometrical meanings of the formula.
