Mixed global anomalies and boundary conformal field theories

Abstract

We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent to gauge them i.e, take the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal boundary state invariant under the action of the center. This also gives conditions on the levels of WZW models. By considering the combined action of the center and charge conjugation on boundary states, we reproduce the condition obtained in the orbifold analysis.

24pages, 1 figure, references added

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• Cluster state as a non-invertible symmetry protected topological phase
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Fermionization of conformal boundary states
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• An Index for Quantum Integrability
• LSM and CPT
• 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
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Emergent Supersymmetry on the Edges
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders