Gauging (3+1)-dimensional topological phases: an approach from surface theories

Abstract

We discuss several bosonic topological phases in (3+1) dimensions enriched by a global ${\mathbb{Z}}_2$ symmetry, and gauging the ${\mathbb{Z}}_2$ symmetry. More specifically, following the spirit of the bulk-boundary correspondence, expected to hold in topological phases of matter in general, we consider boundary (surface) field theories and their orbifold. From the surface partition functions, we extract the modular $\mathcal{S}$ and $\mathcal{T}$ matrices and compare them with $(2+1)$d toplogical phase after dimensional reduction. As a specific example, we discuss topologically ordered phases in $(3+1)$ dimensions described by the BF topological quantum field theories, with abelian exchange statistics between point-like and loop-like quasiparticles. Once the ${\mathbb{Z}}_2$ charge conjugation symmetry is gauged, the ${\mathbb{Z}}_2$ flux becomes non-abelian excitation. The gauged topological phases we are considering here belong to the quantum double model with non-abelian group in $(3+1)$ dimensions.

arXiv comment14 pages, 5 figures

References in corpus (35)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Classification of topological quantum matter with symmetries
• Topological entanglement entropy
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Models for gapped boundaries and domain walls
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Condensate induced transitions between topologically ordered phases
• Genons, twist defects, and projective non-Abelian braiding statistics
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Interacting topological phases and modular invariance
• Symmetry fractionalization and twist defects
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Cheshire charge in (3+1)-D topological phases
• Synthetic Topological Degeneracy by Anyon Condensation
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Changing topology by topological defects in three-dimensional topologically ordered phases
• 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
• 3D Dynamics of 4D Topological BF Theory With Boundary
• From orbifolding conformal field theories to gauging topological phases
• Line defects in Three dimensional Symmetry Protected Topological Phases

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• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence