Symmetry TFT for subsystem symmetry

We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level N in (3 + 1)d as subsystem SymTFT for subsystem ℤ_N symmetry in (2 + 1)d. Focusing on N = 2, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem SL(2, ℤ₂) symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of S-transformation in the subsystem SL(2, ℤ₂), from which the fusion rule of subsystem non-invertible operators can be recovered.