We introduce a method, dubbed the flux-fusion anomaly test, to detect certain
anomalous symmetry fractionalization patterns in two-dimensional symmetry
enriched topological (SET) phases. We focus on bosonic systems with Z2
topological order, and symmetry group of the form G = U(1) ⋊ G', where
G' is an arbitrary group that may include spatial symmetries and/or time
reversal. The anomalous fractionalization patterns we identify cannot occur in
strictly d=2 systems, but can occur at surfaces of d=3 symmetry protected
topological (SPT) phases. This observation leads to examples of d=3 bosonic
topological crystalline insulators (TCIs) that, to our knowledge, have not
previously been identified. In some cases, these d=3 bosonic TCIs can have an
anomalous superfluid at the surface, which is characterized by non-trivial
projective transformations of the superfluid vortices under symmetry. The basic
idea of our anomaly test is to introduce fluxes of the U(1) symmetry, and to
show that some fractionalization patterns cannot be extended to a consistent
action of G' symmetry on the fluxes. For some anomalies, this can be described
in terms of dimensional reduction to d=1 SPT phases. We apply our method to
several different symmetry groups with non-trivial anomalies, including G =
U(1) X Z2T and G = U(1) X Z2P, where Z2T and Z2P are time-reversal and d=2
reflection symmetry, respectively.Comment: 18+13 pages, 4 figures. Significant changes to introduction, and
other changes to improve presentation. Title shortene
