Journal of High Energy Physics (May 2024)

Symmetry TFT for subsystem symmetry

  • Weiguang Cao,
  • Qiang Jia

DOI
https://doi.org/10.1007/JHEP05(2024)225
Journal volume & issue
Vol. 2024, no. 5
pp. 1 – 52

Abstract

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Abstract 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, ℤ 2) symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of S-transformation in the subsystem SL(2, ℤ 2), from which the fusion rule of subsystem non-invertible operators can be recovered.

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