On the Symmetry TFT of Yang-Mills-Chern-Simons theory

Understand

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have non-trivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous.

• This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk.
• First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk.
• Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants.