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Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories · Around

2019

Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories

Ning, Shang-Qiang, Zou, Liujun, Cheng, Meng

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We classify symmetry fractionalization and anomalies in a (3+1)d U(1) gauge theory enriched by a global symmetry group $G$.

We find that, in general, a symmetry-enrichment pattern is specified by 4 pieces of data: $\rho$, a map from $G$ to the duality symmetry group of this $\mathrm{U}(1)$ gauge theory which physically encodes how the symmetry permutes the fractional excitations, $\nu\in\mathcal{H}^2_{\rho}[G, \mathrm{U}_\mathsf{T}(1)]$, the symmetry actions on the electric charge, $p\in\mathcal{H}^1[G, \mathbb{Z}_\mathsf{T}]$, indication of certain domain wall decoration with bosonic integer quantum Hall (BIQH) states, and a torsor $n$ over $\mathcal{H}^3_{\rho}[G, \mathbb{Z}]$, the symmetry actions on the magnetic monopole.
However, certain choices of $(\rho, \nu, p, n)$ are not physically realizable, i.e.
they are anomalous.

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