Gapped phases with non-invertible symmetries: (1+1)d

We propose a general framework to characterize gapped infra-red (IR) phases of theories with non-invertible (or categorical) symmetries. In this paper we focus on (1+1)d gapped phases with fusion category symmetries. The approach that we propose uses the Symmetry Topological Field Theory (SymTFT) as a key input: associated to a field theory in d d spacetime dimensions, the SymTFT lives in one dimension higher and admits a gapped boundary, which realizes the categorical symmetries. It also admits a second, physical, boundary, which is generically not gapped. Upon interval compactification of the SymTFT by colliding the gapped and physical boundaries, we regain the original theory. In this paper, we realize…

• SF
  Simons Foundation

  Award: 724073
• UR
  UK Research and Innovation
• RS
  Royal Society

  Award: URF\R1\231467
• H2
  Horizon 2020

  Awards: 787185, 682608