From orbifolding conformal field theories to gauging topological phases

Abstract

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1) dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function, and predicts the fusion, spin and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual ${\mathbb{Z}}_N$ gauge theory, the twofold symmetric $SU(3{)}_1$, and the $S_3$-symmetric $SO(8{)}_1$ Wess-Zumino-Witten theories.

arXiv comment23 pages, 1 figure

References in corpus (47)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Classification of topological quantum matter with symmetries
• Topological entanglement entropy
• Periodic table for topological insulators and superconductors
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topological Quantum Distillation
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Models for gapped boundaries and domain walls
• Quantum orders in an exact soluble model
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Condensate induced transitions between topologically ordered phases
• A classification of symmetry enriched topological phases with exactly solvable models
• Genons, twist defects, and projective non-Abelian braiding statistics
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Interacting topological phases and modular invariance
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Symmetry fractionalization and twist defects
• Anyon computers with smaller groups
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Quantum symmetries in discrete gauge theories
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Synthetic Topological Degeneracy by Anyon Condensation
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Topological Entanglement Entropy with a Twist
• Boundary States of c=1 and 3/2 Rational Conformal Field Theories
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• The breaking of quantum double symmetries by defect condensation
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Some Correlators of $SU(3{)}_3$ WZW Models on Higher-Genus Riemann Surfaces

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• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging
• Gauging permutation symmetries as a route to non-Abelian fractons
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Gauging (3+1)-dimensional topological phases: an approach from surface theories
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Twofold twist defect chains at criticality
• Dihedral twist liquid models from emergent Majorana fermions
• Partial fillings of the bosonic $E_8$ quantum Hall state
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model