Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry

Clay Cordova; Kantaro Ohmori

doi:10.1103/physrevd.102.025011

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arXiv · 1912.13069

Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry

Clay Cordova·Kantaro Ohmori

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Abstract

We prove that in $(3+1)d$ quantum field theories with $\mathbb{Z}_N$ symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.

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Clay Cordova, Kantaro Ohmori. 2019-12-30. Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry. https://doi.org/10.1103/physrevd.102.025011

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