REVIEW 33 cited by
Duality and defects in rational conformal field theory
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting one-dimensional phase boundaries can be used to extract symmetries and order-disorder dualities of the CFT. The case of central charge c=4/5, for which there are two inequivalent world sheet phases corresponding to the tetra-critical Ising model and the critical three-states Potts model, is treated as an illustrative example.
Forward citations
Cited by 33 Pith papers
-
Lattice non-invertible symmetry from non-commuting transfer matrices
For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
-
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.
-
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 latt...
-
Symmetry extension by condensation defects II: general dimensions and higher-groups
Gauging A×B under a cubic mixed anomaly extends C (n=1) or folds C into a higher-group (n≥2), with the new factor generated by condensation defects and detected via triple-linking.
-
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.
-
Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left...
-
Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
-
Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
-
A new Ising/tricritical-Ising interface: From ${W}_3$ symmetry to Rydberg atoms
A new TIM/Ising conformal interface is identified with emergent W3 symmetry, yielding defect spectrum predictions for Rydberg atom experiments.
-
Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
-
Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
-
Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
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.
-
Exact Quantum Many-Body Scars in 2D Quantum Gauge Models
Exact many-body scar eigenstates of a 2D XY model are mapped via Kramers-Wannier duality to exact scars of a Z2 lattice gauge theory.
-
The tricritical Ising CFT and conformal bootstrap
First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.
-
Noninvertible Symmetry-Enriched Quantum Critical Point
A new class of gapless critical points in 1D, enriched by the noninvertible Rep(D8) symmetry, is constructed via the Kennedy-Tasaki duality and characterized by Ising and compact boson CFTs.
-
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.
-
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.
-
Topological Transition on the Conformal Manifold
Fermionic conformal field theories on a line of couplings can pair up so that opposite sides differ by an invertible topological order, a continuous topological transition that maps to Kramers-Wannier duality after bo...
-
Exact Lindbladian Dynamics from Conformal Embeddings and Topological Defects in Conformal Field Theory
Conformal embeddings and Verlinde defect lines make adjoint Lindbladians triangular or diagonal on natural CFT operator spaces, yielding exact open dynamics.
-
Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies
Spatially modulated symmetries arise from gauging ordinary symmetries under generalized LSM anomalies, with explicit lattice models in 2D and 3D plus field-theoretic descriptions in arbitrary dimensions that connect t...
-
Vertex algebras, topological defects, and Moonshine
Duality defects in the Monster module have an explicit McKay-Thompson formula, and Conway-module defects preserving the N=1 superconformal algebra induce Leech-lattice endomorphisms.
-
Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories
Non-invertible symmetries in finite-group gauge theories are realized as condensation defects, with a complete Z_N dictionary and new automorphism symmetry expressions.
-
Non-invertible twisted compactification of class $\mathcal S$ theory and $(B,B,B)$ branes
Non-invertible twisted compactification of class S theories on S^1 produces 3d N=4 sigma models whose target spaces are fixed-point sets of mapping class group actions on Hitchin moduli space, i.e. (B,B,B) branes.
-
Two-dimensional Anomaly, Orbifolding, and Boundary States
A modular S-transformation criterion on twisted torus partition functions detects zero-form discrete symmetry anomalies in 2D RCFTs, and it matches boundary-state and orbifold conditions in WZW models.
-
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.
-
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.
-
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.
-
Particle-Soliton Degeneracy in 2D Quantum Chromodynamics
In gapped 2D QCD, a broken non-invertible symmetry forces particles and solitons into degenerate multiplets, encoded as quiver diagrams.
-
Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
-
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.
-
Les Houches Lecture Notes on Tensor Networks
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.
-
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.
-
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.
Discussion (0). Continue with ORCID to comment.