Dai-Freed theorem and topological phases of matter

Abstract

We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.

33 pages, 2 figures

References in corpus (7)

• Anomaly polynomial of general 6d SCFTs
• Heisenberg Groups and Noncommutative Fluxes
• Short-range entanglement and invertible field theories
• Classification of abelian spin Chern-Simons theories
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• The global anomalies of (2,0) superconformal field theories in six dimensions
• Index theorem, spin Chern Simons theory and fractional magnetoelectric effect in strongly correlated topological insulators

Cited by in corpus (22)

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• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
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• IIB Explored: Reflection 7-Branes
• The algebra of anomaly interplay
• General anomaly matching by Goldstone bosons
• New Supersymmetric String Theories from Discrete Theta Angles
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Higher Berry Phase of Fermions and Index Theorem
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Atiyah-Patodi-Singer index theorem from axial anomaly
• Twisted Partition Functions as Order Parameters
• Anomaly Inflow and Holography
• Mod-two APS index and domain-wall fermion
• Primordial black holes save $R^2$ inflation
• Anomaly inflow for local boundary conditions
• WIMP Dark Matter from a Natural Discrete Gauge Symmetry in the Standard Model
• Anomaly Inflow of Rarita-Schwinger Field in 3 Dimensions
• Understanding the index theorems with massive fermions
• Anomaly of 4d Weyl fermions with discrete symmetries
• Global Anomalies and Bordism Invariants in One Dimension