New Crosscap States

TL;DR

This paper explores the construction and properties of crosscap states in 2D rational conformal field theories, emphasizing their relation to non-invertible symmetries and Verlinde lines, and extends previous frameworks with new theoretical insights.

Contribution

It introduces a new class of crosscap states labeled by Verlinde lines, generalizes the Cardy condition, and investigates their transformation properties and anomaly connections.

Findings

Existence of crosscap states labeled by Verlinde lines confirmed.

Generalized Cardy condition derived and validated in examples.

Insights into the transformation of crosscaps under Verlinde lines and anomaly relations.

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.