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.

arXiv comment33 pages, 2 figures

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Cited by in corpus (37)

• The "Parity" Anomaly On An Unorientable Manifold
• Dai-Freed anomalies in particle physics
• Anomaly constraints on deconfinement and chiral phase transition
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• On the cobordism classification of symmetry protected topological phases
• Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• On time-reversal anomaly of 2+1d topological phases
• Global anomalies in the Standard Model(s) and Beyond
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• More on time-reversal anomaly of 2+1d topological phases
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Anomaly matching in QCD thermal phase transition
• IIB Explored: Reflection 7-Branes
• The algebra of anomaly interplay
• General anomaly matching by Goldstone bosons
• New Supersymmetric String Theories from Discrete Theta Angles
• The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Anomaly interplay in $U(2)$ gauge theories
• Standard Model as the topological material
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Higher Berry Phase of Fermions and Index Theorem
• Anomaly inflow and $p$-form gauge theories
• 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
• Understanding the index theorems with massive fermions
• Anomaly Inflow of Rarita-Schwinger Field in 3 Dimensions
• WIMP Dark Matter from a Natural Discrete Gauge Symmetry in the Standard Model
• Global Anomalies and Bordism Invariants in One Dimension
• Anomaly of 4d Weyl fermions with discrete symmetries