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

Clay Córdova1,*, Diego García-Sepúlveda1,†, and Kantaro Ohmori2,‡

  • *Contact author: clayc@uchicago.edu
  • †Contact author: dgarciasepulveda@uchicago.edu
  • ‡Contact author: kantaro@hep-th.phys.s.u-tokyo.ac.jp
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Phys. Rev. D 114, 025020 – Published 27 July, 2026

DOI: https://doi.org/10.1103/2m5x-x5dd

Abstract

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, 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 noninvertible one-form symmetry PSU(2)−k at the fixed point. We also discuss theories with Spin(2N) and E7 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.

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Phys. Rev. D 114, 025020– Published 27 July, 2026
  • Received 28 April 2026
  • Accepted 8 July 2026
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