Fermion Path Integrals And Topological Phases

Abstract

Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here, we describe in detail what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples we consider are time-reversal invariant topological insulators and superconductors in 2 or 3 space dimensions. Along the way, we clarify the precise meaning of the statement that in the bulk of a 3d topological insulator, the electromagnetic $\theta$-angle is equal to $\pi$.

67 pp plus appendices, minor corrections in v. 2

References in corpus (5)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Short-range entanglement and invertible field theories
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets

Cited by in corpus (299)

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• Anomalies of fermionic CFTs via cobordism and bootstrap