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The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries (2312.17322v3)

Published 28 Dec 2023 in hep-th, cond-mat.str-el, and math.CT

Abstract: We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework to characterize phase transitions and gapless phases with categorical symmetries. The central tool is the club sandwich, which extends the SymTFT setup to include an interface between two topological orders: there is a symmetry boundary, which is gapped, and a physical boundary that may be gapless, but in addition, there is also a gapped interface in the middle. The club sandwich generalizes so-called Kennedy-Tasaki (KT) transformations. Building on the results in [1, 2] on gapped phases with categorical symmetries, we construct gapless theories describing phase transitions with non-invertible symmetries by applying suitable KT transformations on known phase transitions provided by the critical Ising model and the 3-state Potts model. We also describe in detail the order parameters in these gapless theories characterizing the phase transitions, which are generally mixtures of conventional and string-type order parameters mixed together by the action of categorical symmetries. Additionally, removing the physical boundary from the club sandwiches results in club quiches, which characterize all possible gapped boundary phases with (possibly non-invertible) symmetries that can arise on the boundary of a bulk gapped phase. We also provide a mathematical characterization of gapped boundary phases with symmetries as pivotal tensor functors whose targets are pivotal multi-fusion categories.

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  47. The CFT actually admits an S3subscript𝑆3S_{3}italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT symmetry under which ϵitalic-ϵ\epsilonitalic_ϵ is uncharged. We could thus also regard the 3-state Potts transition as also an S3subscript𝑆3S_{3}italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT-symmetric transition between ℤ3subscriptℤ3\mathbb{Z}_{3}blackboard_Z start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT SSB and trivial phases for S3subscript𝑆3S_{3}italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT symmetry. The additional ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT symmetry does not get spontaneously broken on either side of the transition.
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