Symmetry TFT for Subsystem Symmetry

Understand

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 $\mathbb Z_N$ 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 $SL(2,\mathbb Z_2)$ symmetry of the bulk foliated BF theory.