Two-dimensional Anomaly, Orbifolding, and Boundary States

Abstract

We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines inserted along the nontrivial cycles of two-torus and we propose a criterion to detect the anomaly, which agrees with the truncated modular $S$-matrix approach. The obstruction for orbifolding has been recently interpreted as a mixed anomaly between $G$ and large diffeomorphisms. We clarify the relations among anomaly-free conditions, orbifoldable conditions, and invariant boundary state condition, focusing on Wess-Zumino-Witten models.

45 pages, 2 figures, v2:minor improvement+acknowledgement added

References in corpus (4)

• Generalized Global Symmetries
• Duality and defects in rational conformal field theory
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Anomalies of discrete symmetries in various dimensions and group cohomology

Cited by in corpus (3)

• Fermionization of conformal boundary states
• Symmetry enhancement in RCFT
• Emergent Supersymmetry on the Edges