't Hooft anomalies in symmetry-enriched U(1) gauge theories*

The 3+1D U(1) gauge theory is the effective field theory of a three-dimensional U(1) quantum spin liquid, which is an exotic gapless phase with emergent gapless photon and also gapped fractionalized electric charges and magnetic monopoles. In the presence of global symmetries, these fractionalized excitations can transform in different fractionalization patterns, which can be captured by projective representations of the symmetry group. Symmetry properties of these gapped excitations determine the universal properties of a symmetric U(1) quantum spin liquid, as well as the nature of its proximate phases. However, certain patterns of symmetry fractionalization cannot be realized in strictly 3+1D . Instead, they can only be realized on the boundary of 4+1D symmetry-protected topological phases. This type of symmetry fractionalization patterns are referred to as possessing 't Hooft anomalies. We obtain the classification of the patterns of symmetry fractionalization in symmetry-enriched U(1) gauge theories, and, in particular, an explicit formula to determine the relevant 't Hooft anomalies in terms of the fractionalization patterns.