Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
Symmetry TFTs from string theory
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The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
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Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
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Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.