Non-invertible one-form symmetries are naturally realized in (2+1) d topological quantum field theories. In this work, we consider the potential realization of such symmetries in (2+1) d conformal field theories, investigating whether gapless systems can exhibit similar symmetry structures. To that end, we discuss transitions between topological field theories in (2+1) d which are driven by the Higgs mechanism in Chern-Simons matter theories. Such transitions can be modeled mesoscopically by filling spacetime with a lattice-shaped domain wall network separating the two topological phases. Along the domain walls are coset conformal field theories describing gapless chiral modes trapped by a locally vanishing scalar mass. In this presentation, the one-form symmetries of the transition point can be deduced by using anyon condensation to track lines through the domain wall network. Using this framework, we discuss a variety of concrete examples of non-invertible one-form symmetry in fixed-point theories. For instance, SU (k) ₂ Chern-Simons theory coupled to a scalar in the symmetric tensor representation produces a transition from an SU (k) ₂ phase to an SO (k) ₄ phase and has non-invertible one-form symmetry PSU (2) -₊ at the fixed point. We also discuss theories with Spin (2N) and E₇ gauge groups manifesting other patterns of non-invertible one-form symmetry. In many of our examples, the non-invertible one-form symmetry is not a modular invariant TQFT on its own and thus is an intrinsic part of the fixed-point dynamics.
Córdova et al. (Fri,) studied this question.