Higher central charges and topological boundaries in 2+1-dimensional TQFTs

Abstract

A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the chiral central charge $c_{-}$ has to vanish. In this paper, we consider conditions associated with "higher" central charges, which have been introduced recently in the math literature. In terms of these new obstructions, we identify necessary and sufficient conditions for the existence of a topological boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the identification of a Lagrangian subgroup. Our proof relies on general aspects of gauging generalized global symmetries. For non-Abelian TQFTs, we give a geometric way of studying topological boundary conditions, and explain certain necessary conditions given again in terms of the higher central charges. Along the way, we find a curious duality in the partition functions of Abelian TQFTs, which begs for an explanation via the 3d-3d correspondence.

arXiv comment51 pages. v2: minor clarifications and references added

References in corpus (61)

• Anyons in an exactly solved model and beyond
• Generalized Global Symmetries
• String-net condensation: A physical mechanism for topological phases
• Symmetries and Strings in Field Theory and Gravity
• Coupling a QFT to a TQFT and Duality
• Models for gapped boundaries and domain walls
• TFT construction of RCFT correlators I: Partition functions
• Condensate induced transitions between topologically ordered phases
• On finite symmetries and their gauging in two dimensions
• On gauging finite subgroups
• Symmetries and Strings of Adjoint QCD${}_2$
• Orbifold groupoids
• Protected edge modes without symmetry
• Topological boundary conditions in abelian Chern-Simons theory
• On 2-Group Global Symmetries and Their Anomalies
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• D-brane Charges in Five-brane backgrounds
• TFT construction of RCFT correlators III: Simple currents
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Anyon condensation and its applications
• Defect lines, dualities, and generalised orbifolds
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• A theory of 2+1D bosonic topological orders
• Cluster decomposition, T-duality, and gerby CFT's
• Classification of Topological Defects in Abelian Topological States
• Setting the quantum integrand of M-theory
• Orbifold completion of defect bicategories
• Congruence Property In Conformal Field Theory
• D-branes and K-theory in 2D topological field theory
• The kernel of the modular representation and the Galois action in RCFT
• Modified instanton sum in QCD and higher-groups
• Boundary Degeneracy of Topological Order
• Generalized string-net models: A thorough exposition
• Phases Of Adjoint QCD${}_3$ And Dualities
• Turaev-Viro invariants as an extended TQFT
• Ground State Degeneracy of Topological Phases on Open Surfaces
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Classification of abelian spin Chern-Simons theories
• Ground-state degeneracy for abelian anyons in the presence of gapped boundaries
• On two approaches to 3-dimensional TQFTs
• Anomalous Symmetries End at the Boundary
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Discrete torsion defects
• Hecke Relations in Rational Conformal Field Theory
• Gapped boundary theories in three dimensions
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• M-theoretic Genesis of Topological Phases
• Classification and construction of unitary topological field theories in two dimensions
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Path-integral invariants in abelian Chern-Simons theory
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Higher Gauss sums of modular categories
• Higher central charges and Witt groups
• Orbifolds of Reshetikhin-Turaev TQFTs
• Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Condensations in higher categories
• A remark on gapped domain walls between topological phases
• Galois Conjugation and Multiboundary Entanglement Entropy
• On framings of links in 3-manifolds

Cited by in corpus (51)

• Non-Invertible Duality Defects in 3+1 Dimensions
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Dualities in one-dimensional quantum lattice models: topological sectors
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Pauli stabilizer models of twisted quantum doubles
• Bootstrapping Non-Invertible Symmetries
• Modular commutator in gapped quantum many-body systems
• Duality Defects in $E_8$
• Pauli topological subsystem codes from Abelian anyon theories
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Exact emergent higher-form symmetries in bosonic lattice models
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• The holography of non-invertible self-duality symmetries
• Holographic duals of symmetry broken phases
• Extracting higher central charge from a single wave function
• Symmetry-preserving boundary of (2+1)D fractional quantum Hall states
• Ising-like and Fibonacci-Anyons from KZ-equations
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Higher Gauge Theory
• 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
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Conformal geometry from entanglement
• Gapped boundaries of fermionic topological orders and higher central charges
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Non-invertible symmetries in finite-group gauge theory
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Non-Invertible Gauss Law and Axions
• Soft symmetries of topological orders
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Magic Boundaries of 3D Color Codes
• Fermionic defects of topological phases and logical gates
• $N$-ality symmetry and SPT phases in (1+1)d
• Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order
• Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator
• Proliferation transitions from a topological phase in $2+1$ dimensions
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs
• Factorization and global symmetries in holography