Anomaly indicator of rotation symmetry in (3+1)D topological order

Ryohei Kobayashi; Ken Shiozaki

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arXiv · 1901.06195

Anomaly indicator of rotation symmetry in (3+1)D topological order

Ryohei Kobayashi·Ken Shiozaki

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Abstract

We examine (3+1)D topological ordered phases with $C_k$ rotation symmetry. We show that some rotation symmetric (3+1)D topological orders are anomalous, in the sense that they cannot exist in standalone (3+1)D systems, but only exist on the surface of (4+1)D SPT phases. For (3+1)D discrete gauge theories, we propose anomaly indicator that can diagnose the $\mathbb{Z}_k$ valued rotation anomaly. Since (3+1)D topological phases support both point-like and loop-like excitations, the indicator is expressed in terms of the symmetry properties of point and loop-like excitations, and topological data of (3+1)D discrete gauge theories.

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Ryohei Kobayashi, Ken Shiozaki. 2019-01-18. Anomaly indicator of rotation symmetry in (3+1)D topological order. https://arxiv.org/abs/1901.06195

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