2025/05/28 by Jia, Qiang, Jia, Zhian · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2505.22261
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a d-dimensional theory and topological order in a (d+1)-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For (2+1)D gapped phases, we introduce a 2-foliated (3+1)D exotic tensor gauge theory (which is equivalent to 2-foliated (3+1)D BF theory via exotic duality) as the subsystem SymTFT and systematically analyze its topological boundary conditions and linearly rigid subsystem symmetries. Taking subsystem symmetry groups G = ℤN and G=ℤN × ℤM as examples, we demonstrate how to recover the classification scheme C[G] = H2(G× 2, U(1)) / ( H2(G, U(1)) )3, which was previously derived by examining topological invariant under linear subsystem-symmetric local unitary transformations in the lattice Hamiltonian formalism. To illustrate the correspondence between field-theoretic and lattice descriptions, we further analyze ℤ2 × ℤ2 and ℤN × ℤM cluster state models as concrete examples.