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Anomaly Inflow and the $\eta$-Invariant

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arxiv 1909.08775 v3 pith:YCDCJZHQ submitted 2019-09-19 hep-th cond-mat.str-elhep-lathep-phmath-phmath.MP

Edward Witten , Kazuya Yonekura This is my paper
classification hep-thcond-mat.str-elhep-lathep-phmath-phmath.MP
keywords invariantanomaliesperturbativeanomalyinflownonperturbativebeenchern-simons
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Perturbative fermion anomalies in spacetime dimension $d$ have a well-known relation to Chern-Simons functions in dimension $D=d+1$. This relationship is manifested in a beautiful way in "anomaly inflow" from the bulk of a system to its boundary. Along with perturbative anomalies, fermions also have global or nonperturbative anomalies, which can be incorporated by using the $\eta$-invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function. Here we give a nonperturbative description of anomaly inflow, involving the $\eta$-invariant. This formula has been expected in the past based on the Dai-Freed theorem, but has not been fully justified. It leads to a general description of perturbative and nonperturbative fermion anomalies in $d$ dimensions in terms of an $\eta$-invariant in $D$ dimensions. This $\eta$-invariant is a cobordism invariant whenever perturbative anomalies cancel.

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Cited by 5 Pith papers

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  3. The absence of global anomalies of CP symmetry

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  4. Non-supersymmetric branes and discrete topological terms

    hep-th 2025-07 conditional novelty 6.0 of 10

    A direct computation from the tentative NS5-brane spectrum gives the opposite Z3 topological term (1/3 vs 2/3) from Tachikawa-Zhang, so the spectrum or the inflow interpretation must change.

  5. Anomalous Bulk Current in Quantum Hall Systems with an Expanding Edge

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    For a quantum Hall system with an expanding edge, the authors show the edge carries a covariant gravitational anomaly and the bulk carries an equal and opposite integrated energy flux.

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