论文标题
mod-two aps索引和域壁费米昂
Mod-two APS index and domain-wall fermion
论文作者
论文摘要
我们使用域壁费米昂以物理学家的方式重新制定了Mod-Two Atiyah-Patodi-Singer（APS）索引。我们的新配方是在封闭的歧管上给出的，该歧管从与边界的原始歧管延伸，而我们给出了一个fermion质量术语，在原始边界的位置更改其标志。这种新的设置不需要APS边界条件，该条件是非本地的。两种不同公式之间的数学证明是通过对较高维歧管的狄拉克运算符相同索引的两个不同评估给出的。域壁式费米恩使我们能够以天然的方式分离边缘和散装模式，但不会以规格不变的方式分离，从而简单地描述了全球异常流入的简单描述。
We reformulate the mod-two Atiyah-Patodi-Singer (APS) index in a physicist-friendly way using the domain-wall fermion. Our new formulation is given on a closed manifold, which is extended from the original manifold with boundary, where we instead give a fermion mass term changing its sign at the location of the original boundary. This new setup does not need the APS boundary condition, which is non-local. A mathematical proof of equivalence between the two different formulations is given by two different evaluations of the same index of a Dirac operator on a higher dimensional manifold. The domain-wall fermion allows us to separate the edge and bulk mode contributions in a natural but not in a gauge invariant way, which offers a straightforward description of the global anomaly inflow.
