Higgsing transitions from topological field theory and noninvertible symmetry in Chern-Simons matter theories

Noninvertible 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 noninvertible one-form symmetry in fixed-point theories. For instance, S U ( k ) 2 Chern-Simons theory coupled to a scalar in the symmetric tensor representation produces a transition from an S U ( k ) 2 phase to an S O ( k ) 4 phase and has noninvertible one-form symmetry PSU ( 2 ) − k at the fixed point. We also discuss theories with Spin ( 2 N ) and E 7 gauge groups manifesting other patterns of noninvertible one-form symmetry. In many of our examples, the noninvertible one-form symmetry is not a modular invariant topological quantum field theory on its own and thus is an intrinsic part of the fixed-point dynamics.