Fracton Topological Holography

• URL: http://arxiv.org/abs/2606.03582v1
• Date: Tue, 02 Jun 2026 12:50:55 GMT
• Title: Fracton Topological Holography
• Abstract summary: Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension.<n>We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes.
• Score: 17.34734174427962
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension. We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes. The construction is organized as a general four-stage framework: prepare the bulk model and compute its excitations, determine boundary data and admissible gapped top boundaries, identify the low-energy preserving operator algebra together with its symmetry, relation, and twist data, and then switch among top boundaries to compare the induced boundary descriptions. As a type-I example, we develop FTH for the X-cube model with smooth and rough top boundaries; for a minimal effective Hamiltonian, both yield transverse-field plaquette Ising models, with exchanged subsystem symmetry and twist data, and the boundary switch is implemented by a linear-depth local unitary sequential quantum circuit (SQC). As a type-II example, we formulate FTH for Haah's cubic code in the Laurent-polynomial stabilizer formalism and analyze the natural $(Z)$ and $(X)$ top boundaries, which induce two two-dimensional qubit systems related locally by exchanging generalized plaquette Ising and transverse-field terms and nonlocally by a symmetry--relation duality. These results show that FTH is a genuine extension of TH to both type-I and type-II fracton orders. FTH therefore provides a concrete framework for organizing and understanding duality, with the prospect of offering a systematic route to new dualities.

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