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.
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Generalized twisted partition functions
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abstract
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
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UNVERDICTED 17representative citing papers
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
Tensor renormalization group computes symmetry-twisted partition functions to identify critical points solely from them, yielding Tc=2.2017(2) and nu=0.663(33) for the 3D O(2) model plus TBKT=0.8928(2) for the 2D O(2) BKT transition.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
Derives additivity and fusion rules for defect g-functions in integrable 2D QFT, with effective amplitudes for non-topological cases and lowered entropy contribution in Ising non-topological fusion.
Topological defects constrain the allowed RG flows of N=1 superconformal minimal models, first via a bosonic coset description and then for the full superconformal case.
Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
Lattice realizations of topological defects in non-unitary 2D CFTs are built from modified RSOS models, yielding numerical results that match analytical predictions for spectra and RG flows.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
citing papers explorer
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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.
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Non-Invertible Duality Defects in 3+1 Dimensions
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
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Protected operators in non-local defect CFTs from AdS
Defect-induced symmetry breaking viewed from the AdS bulk enforces protected displacement and tilt operators in non-local boundary CFTs via Ward identities.
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Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
Tensor renormalization group computes symmetry-twisted partition functions to identify critical points solely from them, yielding Tc=2.2017(2) and nu=0.663(33) for the 3D O(2) model plus TBKT=0.8928(2) for the 2D O(2) BKT transition.
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Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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From gauging to duality in one-dimensional quantum lattice models
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
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Fusion of Integrable Defects and the Defect $g$-Function
Derives additivity and fusion rules for defect g-functions in integrable 2D QFT, with effective amplitudes for non-topological cases and lowered entropy contribution in Ising non-topological fusion.
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Defects in N=1 minimal models and RG flows
Topological defects constrain the allowed RG flows of N=1 superconformal minimal models, first via a bosonic coset description and then for the full superconformal case.
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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.
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Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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Lattice Topological Defects in Non-Unitary Conformal Field Theories
Lattice realizations of topological defects in non-unitary 2D CFTs are built from modified RSOS models, yielding numerical results that match analytical predictions for spectra and RG flows.
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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.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.