New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
Canonical reference
Title resolution pending
Canonical reference. 100% of citing Pith papers cite this work as background.
25
Pith papers citing it
Background
100% of classified citations
citation-role summary
background 8
citation-polarity summary
roles
background 8polarities
background 8representative citing papers
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.
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
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.
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
Introduces tube-sector probabilities from the center of boundary tube algebras to give optimal one-shot distinguishability of quantum states under generalized symmetries.
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
-
Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
-
Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
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.
-
Invariants of Sequential Circuits and Generalized Non-Abelian Statistics
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
-
Fracton Topological Holography
Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
-
Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
-
A Twist on Scattering from Defect Anomalies
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
-
SymTFT in Superspace
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
-
Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
-
On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
-
SymTFT construction of gapless exotic-foliated dual models
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.
-
Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
-
Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
-
Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
-
Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
-
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.
-
Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
-
The Line, the Strip and the Duality Defect
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
-
Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries
Introduces tube-sector probabilities from the center of boundary tube algebras to give optimal one-shot distinguishability of quantum states under generalized symmetries.
-
Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
-
When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
-
Global symmetries: locality, unitarity, and regularity
Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.
-
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
-
ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
-
Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
- Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models