Anomaly inflow for local boundary conditions
arXiv:2208.00476 · doi:10.1007/JHEP09(2022)250
Abstract
We study the -invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to -invariants of a boundary Dirac operator, while in odd dimension, it is expressed through the index of boundary operators. We stress the necessity of the strong ellipticity condition for the applicability of our methods. We show that the Witten--Yonekura boundary conditions are not strongly elliptic, though they are very close to strongly elliptic ones.
arXiv comment19 pages, V2: misprints corrected, comments added
References in corpus (21)
- Heat kernel expansion: user's manual
- Fermion Path Integrals And Topological Phases
- Eta-Invariants and Determinant Lines
- Effective QED Actions: Representations, Gauge Invariance, Anomalies and Mass Expansions
- Dai-Freed theorem and topological phases of matter
- Gauge Theories in a Bag
- Gravitational parity anomaly with and without boundaries
- Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary
- Parity anomaly in four dimensions
- The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
- Strong ellipticity and spectral properties of chiral bag boundary conditions
- Index Theorems and Domain Walls
- Anomalies of non-Abelian finite groups via cobordism
- Stability theorems for chiral bag boundary conditions
- Fractional Fermion Number and Hall Conductivity of Domain Walls
- How many surface modes does one see on the boundary of a Dirac material?
- Atiyah-Patodi-Singer Index Theorem for Domain Walls
- Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
- Spectral asymmetry on the ball and asymptotics of the asymmetry kernel
- Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase
- Index Theorem for Domain Walls