Non-invertible symmetries in finite-group gauge theory

Abstract

We investigate the invertible and non-invertible symmetries of topological finite-group gauge theories in general spacetime dimensions, where the gauge group can be abelian or non-abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d ${\mathbb{Z}}_2$ gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-abelian finite-group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.

arXiv comment55 pages, 20 figures. V2: fixed figures misprints and typos. V3: published version - fixed typos, hyphenization rules, notation used for D4 action

References in corpus (72)

• Fault-tolerant quantum computation by anyons
• Generalized Global Symmetries
• Lieb-Schultz-Mattis in Higher Dimensions
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Coupling a QFT to a TQFT and Duality
• Models for gapped boundaries and domain walls
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Superconductors are topologically ordered
• On finite symmetries and their gauging in two dimensions
• A classification of symmetry enriched topological phases with exactly solvable models
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Higher Gauging and Non-invertible Condensation Defects
• Topological boundary conditions in abelian Chern-Simons theory
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Non-Invertible Higher-Categorical Symmetries
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• On the classification of topological orders
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Dynamically Generated Logical Qubits
• Foliated fracton order from gauging subsystem symmetries
• Quantum groups and nonabelian braiding in quantum Hall systems
• Finite Group Modular Data
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Symmetry fractionalization and twist defects
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Foliated Quantum Field Theory of Fracton Order
• Fractional excitations in foliated fracton phases
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Cheshire charge in (3+1)-D topological phases
• A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions
• Tube algebras, excitations statistics and compactification in gauge models of topological phases
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Anomalies of non-invertible self-duality symmetries: fractionalization and gauging
• Boundary theory of the X-cube model in the continuum
• Lattice Models for Phases and Transitions with Non-Invertible Symmetries
• String Condensations in 3+1D and Lagrangian Algebras
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders
• Gapped boundaries of (3+1)d topological orders
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
• Confinement in partially broken abelian Chern-Simons theories
• String operators for Cheshire strings in topological phases
• Illustrating the Categorical Landau Paradigm in Lattice Models
• Fermionic defects of topological phases and logical gates
• Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories
• Gapped Interfaces in Fracton Models and Foliated Fields

Cited by in corpus (2)

• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier