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Decomposition, condensation defects, and fusion

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arxiv 2208.05982 v2 pith:PF3OCTJX submitted 2022-08-11 hep-th cond-mat.str-el

Ling Lin , Daniel G. Robbins , Eric Sharpe This is my paper · ORCID
classification hep-thcond-mat.str-el
keywords decompositioncondensationdefectsfusionfieldhigher-formquantumsymmetries
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In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d-dimensional quantum field theories with global (d-1)-form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non-invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher-form symmetries, which can be used to select individual universes in a decomposition.

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Cited by 5 Pith papers

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

  1. Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

    hep-th 2025-07 conditional novelty 7.0 of 10

    A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.

  2. Notes on (-2)-form symmetries

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    For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.

  4. Information Loss in Generalized Symmetry Breaking

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    Anyon condensation is encoded as a conditional expectation between operator algebras, and the information it erases, measured by relative entropy, is claimed to be bounded by the log of the condensate's quantum dimension.

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    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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