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

TL;DR

This paper investigates the Symmetry TFT of 3D Yang-Mills-Chern-Simons theory, resolving puzzles related to non-trivial braiding and global variants by incorporating endable surfaces, and confirms findings through holographic methods.

Contribution

It introduces the inclusion of endable surfaces in the bulk topological operators to accurately describe the symmetry and anomalies of the theory.

Findings

Resolved puzzles about braiding and boundary conditions in the Symmetry TFT.

Reproduced all global variants of the theory with correct symmetries and anomalies.

Validated the approach with a holographic realization.

Abstract

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. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.