New Crosscap States

Abstract

We investigate crosscap states in two-dimensional rational conformal field theories (RCFTs), with an emphasis on the role of non-invertible symmetries. In particular, we argue for the existence of crosscap states labelled by each Verlinde line in the RCFT, extending previous constructions involving simple currents. Evidence for the existence of these new states is obtained by deriving a generalized Cardy condition incorporating both crosscaps and topological defects, which we check in some concrete examples. Finally, we briefly discuss how these crosscap states transform under the action of Verlinde lines, as well as the connection to mixed anomalies between parity and internal symmetries.

33 pages

References in corpus (13)

• Anyons in an exactly solved model and beyond
• Generalized Global Symmetries
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• TFT construction of RCFT correlators I: Partition functions
• On finite symmetries and their gauging in two dimensions
• TFT construction of RCFT correlators II: Unoriented world sheets
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Topological field theories and symmetry protected topological phases with fusion category symmetries
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Notes on Orientifolds of Rational Conformal Field Theories
• Unoriented 3d TFTs
• Loop Algorithm for Quantum Transverse Ising Model in a Longitudinal Field

Cited by in corpus (1)

• No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$