Candidate gaugings of categorical continuous symmetry

A bstract Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable sub-symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category Cᵏ(G) C k G associated to a QFT with continuous global G -symmetry and possible ’t Hooft anomaly labeled by an integer k . We use the combination of the BF theory and the level- k Chern-Simons theory with gauge group G as a semiclassical kernel-theoretic working model for the corresponding SymTFT. Under two explicit working assumptions, namely that this BF + k CS theory provides the relevant SymTFT model and that the common +1 eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular S - and T -kernels from Hopf-link and framing correlators in S 3 semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups.