Dualities between 2+1d fusion surface models from braided fusion categories, by Luisa Eck
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SciPost Physics Home Authoring Refereeing Submit a manuscript About Dualities between 2+1d fusion surface models from braided fusion categories Luisa Eck SciPost Phys. 19, 157 (2025) · published 17 December 2025 doi: 10.21468/SciPostPhys.19.6.157 pdf BiBTeX RIS Submissions/Reports Abstract Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.6.157TI - Dualities between 2+1d fusion surface models from braided fusion categoriesPY - 2025/12/17UR - https://scipost.org/SciPostPhys.19.6.157JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 6SP - 157A1 - Eck, LuisaAB - Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.ER - × @Article{10.21468/SciPostPhys.19.6.157, title={{Dualities between 2+1d fusion surface models from braided fusion categories}}, author={Luisa Eck}, journal={SciPost Phys.}, volume={19}, pages={157}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.6.157}, url={https://scipost.org/10.21468/SciPostPhys.19.6.157},} Ontology / Topics See full Ontology or Topics database.
Anyons Dualities Author / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Luisa Eck 1 Rudolf Peierls Centre for Theoretical Physics Funders for the research work leading to this publication Engineering and Physical Sciences Research Council [EPSRC] National Science Foundation [NSF]