2021/11/22 by Fukaya, Hidenori, Furuta, Mikio, Matsuki, Yoshiyuki +4
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2111.11040
Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah- Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, with which the physical roles of edge/bulk modes are unclear and how the causality of the theory is maintained is not obvious. In this work, we consider a special case where the Dirac operator is in a real representation and its eta invariant becomes the mod-two type APS index. We propose a physicist-friendly reformulation of the mod-two index using domain-wall fermion formalism, which naturally describes how the global anomaly is canceled between edge and bulk.