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Résumé |
Phases of matter and the transitions between them are famously characterized within the Landau paradigm and Landau-Ginzburg theory: phases are labeled by broken or unbroken symmetries, while phase transitions are described in terms of scalar order parameters. There are, however, phases beyond the standard Landau paradigm that are distinguished not by the realization of ordinary symmetries, but by that of generalized global symmetries. Among these, topologically ordered phases in $(2+1)d$ possess non-invertible 1-form symmetries described by anyon lines. In this talk, I will present a framework for describing transitions between topologically ordered phases related by anyon proliferation, which can be viewed as a non-invertible generalization of the choice of the unbroken symmetry. The resulting theories involve scalar fields coupled to gauge fields. A crucial ingredient in this construction is the $(3+1)d$ Symmetry Topological Field Theory (SymTFT), which allows to separate symmetry from dynamics and will be employed in a rather unconventional way. |
