Fermion Path Integrals And Topological Phases
By E. Witten. 2015
405 citations recorded by the source corpus.
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 -angle is equal to .
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/8895805951bd341b0f2fbc3d98e189ec60309731
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- JT gravity and the ensembles of random matrix theory (2019, background): “This is schematically explained in section 5 of [76].”
- Gapped boundary phases of topological insulators via weak coupling (2016, methodology): “The path integral of the topological insulator can be analyzed [60, 17] by using the APS theorem for the index23 I of the Dirac operator on X:”
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- The Swampland: Introduction and Review (2019, background): “This leads then to additional constraints on the theory [386–388].”
- Chern-Simons-matter dualities with SO and USp gauge groups (2016, background): “Let us start by reviewing some facts about the fermion determinant [64,65] and our notation.”
- Theta, time reversal and temperature (2017, positive): “We can either couple it to a U(1) gauge field and thus break time reversal invariance (this is what happens when we choose the fermion path integral phase to be given by a half of the η-invariant, see [64]) or we can add a four-dimensional bulk with θ = π and retain the time reversal symmetry as wel”
- Dai-Freed anomalies in particle physics (2018, background): “Spincand Spin spacetimes. 2 Review In this section we will brie y review the necessary background that we will use later on. Excellent introductory references are [8{10] for traditional anomalies and [6] for the new ones. We also recommend [11] for an introduction to some of the notions in algebraic”
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