Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids

Understand

Topological spin liquids can be described by topological gauge theories with global symmetry.

• Due to the presence of both nontrivial bulk deconfined gauge fluxes and global symmetry, topological spin liquids are examples of the so-called "Symmetry Enriched Topological phases" (SET).
• In this paper, we find that, in some twisted versions of topological gauge theories (with discrete Abelian gauge group $G_g$), implementing a global symmetry (denoted by $G_s$) is anomalous although symmetry charge carried by topological point-like excitations is normally fractionalized and classified by the second cohomology group.
• To demonstrate the anomaly, we fully gauge the global symmetry, rendering a new gauge theory that is not gauge invariant.