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Boundary SymTFT

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arxiv 2409.02166 v2 pith:FXGG33KR submitted 2024-09-03 hep-th cond-mat.str-elmath-phmath.CTmath.MP

Lakshya Bhardwaj , Christian Copetti , Daniel Pajer , Sakura Schafer-Nameki This is my paper · ORCID
classification hep-thcond-mat.str-elmath-phmath.CTmath.MP
keywords boundaryconditionspropertiessymmetrysymtfttopologicalcategoricalcharges
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abstract

We study properties of boundary conditions (BCs) in theories with categorical (or non-invertible) symmetries. We describe how the transformation properties, or (generalized) charges, of BCs are captured by topological BCs of Symmetry Topological Field Theory (SymTFT), which is a topological field theory in one higher spacetime dimension. As an application of the SymTFT chracterization, we discuss the symmetry properties of boundary conditions for (1+1)d gapped and gapless phases. We provide a number of concrete examples in spacetime dimensions $d=2,3$. We furthermore expand the lattice description for (1+1)d anyon chains with categorical symmetries to include boundary conditions carrying arbitrary 1-charges under the symmetry.

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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    hep-th 2026-08 conditional novelty 7.0 of 10

    For G=(Z2,Z2,triv,1), the authors classify anomalies via oriented and spin bordism in spacetime dimensions d<=5 and derive the (3+1)D SymTFT boundary conditions, including the equivalence of the anomalous symmetry cat...

  2. Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging

    hep-th 2026-07 accept novelty 7.0 of 10

    Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.

  3. Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes

    quant-ph 2025-12 conditional novelty 7.0 of 10

    Non-Abelian surface codes based on dihedral groups D_{4N} implement transversal phase gates T^{1/N} at any Clifford-hierarchy level in 2D, with a qubit-only version when 8N is a power of two.

  4. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...

  5. SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking

    hep-th 2025-09 conditional novelty 6.0 of 10

    Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.

  6. An Algebraic Theory of Gapped Domain Wall Partons

    cond-mat.str-el 2025-06 conditional novelty 6.0 of 10

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  7. Higher Representations and Quark Confinement

    hep-th 2025-01 conditional novelty 6.0 of 10

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    hep-th 2025-01 conditional novelty 6.0 of 10

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    hep-th 2024-11 conditional novelty 6.0 of 10

    The authors derive partition functions of orbifolded, fermionized, and para-fermionized 2D CFTs from topological boundary states of the 3D SymTFT, introducing para-fermionic Lagrangian algebras.

  10. SymTFTs for $U(1)$ symmetries from descent

    hep-th 2024-11 conditional novelty 6.0 of 10

    Symmetry descent is extended from discrete to continuous U(1) higher-form symmetries, yielding SymTFTs that match the Antinucci-Benini and Brennan-Sun constructions.

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    hep-th 2025-09 conditional novelty 5.0 of 10

    Constructs AKSZ sandwich SymTFTs with stacky target spaces that encode the center symmetries of Chern-Simons, Yang-Mills, and MacDowell-Mansouri gravity.

  12. Unitary Categorical Symmetries

    hep-th 2025-02 conditional novelty 5.0 of 10

    The paper proposes that twisted-sector local operators transform in *-representations of the tube algebra of a higher fusion category symmetry, and classifies these representations using higher S-matrices.

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