The paper presents a generalization of the SymTFT framework to study phase transitions and gapless phases with categorical symmetries. The central concept is the "club sandwich", which extends the SymTFT setup to include an interface between two topological orders.
The key points are:
Gapped boundary phases with non-invertible symmetries are characterized by the "club quiche", which couples a (d+1)-dimensional TQFT to the SymTFT via a topological interface.
Phase transitions between gapped phases with categorical symmetries are described by the "club sandwich", which provides a map between two SymTFTs via a non-maximal condensable algebra interface. This generalizes the Kennedy-Tasaki (KT) transformation.
The authors construct new gapless phases and phase transitions by applying suitable KT transformations on known phase transitions, such as the critical Ising model and 3-state Potts model. The order parameters in these gapless theories are generally mixtures of conventional and string-type order parameters.
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.
The authors 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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by Lakshya Bhar... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2312.17322.pdfDeeper Inquiries