Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions

• URL: http://arxiv.org/abs/2609.06751v1
• Date: Sun, 06 Sep 2026 17:49:44 GMT
• Title: Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions
• Abstract summary: In (1+1)D, "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries.<n>How to extract the universal dynamical properties of the transitions from this understanding?<n>The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters.
• Score: 6.359700736554043
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep($S_3$) symmetry.

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