论文标题
Atiyah-Patodi-Singer指数的晶格公式
A lattice formulation of the Atiyah-Patodi-Singer index
论文作者
论文摘要
由于Hasenfratz等人的开创性工作，可以很好地理解了没有边界的晶格上的Atiyah-Singer索引定理。但是，它扩展到具有边界的系统（所谓的Atiyah-Patodi-Singer索引定理），在3+1维拓扑事项中，在3+1维拓扑事项中取消T-反对在取消T-反对作用中起着至关重要的作用，仅在连续性理论中才知道，并且没有在远处实现。在这项工作中，我们尝试非扰动地定义3+1维中的晶格域壁费米子的替代索引。我们将证明该新索引在连续限制中，将其收敛到与边界上的歧管上定义的Atiyah-Patodi-Singer索引，该指数与域壁的表面相吻合。
Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz et al. But its extension to the system with boundary (the so-called Atiyah- Patodi-Singer index theorem), which plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and no lattice realization has been made so far. In this work, we try to non-perturbatively define an alternative index from the lattice domain-wall fermion in 3+1 dimensions. We will show that this new index in the continuum limit, converges to the Atiyah-Patodi-Singer index defined on a manifold with boundary, which coincides with the surface of the domain-wall.
