IAS CMT/QFT Group Meeting

Abstract: Recently, the notion of symmetry has been generalized by relaxing the codimensions, invertibility and topologicalness of the symmetry operators. In this talk, I will introduce a new generalization, subsystem non-invertible symmetry, by lifting both the invertibility and topologicalness of the ordinary global symmetry.  After reviewing the simplest non-invertible symmetry in (1+1)d from the Kramers-Wannier (KW) duality, I will explore non-invertible symmetries in two-dimensional lattice models with subsystem Z_2 symmetry by introducing a subsystem Z_2-gauging procedure, called the subsystem KW transformation. The subsystem Z_2 symmetry in (2+1)d can be captured by the topological boundaries of a (3+1)d 2-foliated theory, which serves as subsystem generalization of symmetry topological field theory (SymTFT). We further study the duality transformations on the boundary theory from a bulk point of view through the corresponding condensation defects in the subsystem SymTFT.