Characterize conformal crosscap states in conformal field theories

Determine precise and complete criteria for which states qualify as conformal crosscap states in 1+1-dimensional conformal field theories, including a full characterization based on sewing conditions and loop–tree channel correspondence, so that the set of admissible conformal crosscap states is unambiguously specified.

Background

Crosscap states encode the physics of non-orientable manifolds (e.g., the Klein bottle) within conformal field theory and are expected to satisfy sewing conditions and loop–tree channel equivalence. Despite progress in boundary CFT and studies of crosscap coefficients, the authors note that the foundational question of what constitutes an admissible conformal crosscap state has not been fully resolved.

Clarifying the defining criteria would enable systematic construction and usage of crosscap states across CFTs, underpinning applications such as extracting universal parameters from single wave functions and connecting continuum CFT descriptions with lattice realizations.