论文标题
域墙的Atiyah-Patodi-Singer索引定理
Atiyah-Patodi-Singer Index Theorem for Domain Walls
论文作者
论文摘要
我们将Dirac运算符的索引在紧凑的尺寸歧管上带有域壁。后者被定义为连接跳跃的共同维度一个子手法。我们制定并证明了Atiyah-Patodi-singer定理的类似物，该定理将索引与Pontryagin密度的批量积分和$η$ invariants的批量积分相关联。因此，该指数通过体积的全局性手性异常表达，壁上的奇偶元异常。
We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the Atiyah-Patodi-Singer theorem that relates the index to the bulk integral of Pontryagin density and $η$-invariants of auxiliary Dirac operators on the domain wall. Thus the index is expressed through the global chiral anomaly in the volume and the parity anomaly on the wall.
