Minimal defining data for CFTs in general spacetime dimensions

Determine, in general spacetime dimensions, a minimal set of defining data for a conformal field theory that suffices to deduce all correlation functions on arbitrary manifolds, noting that such a set may not be unique.

Background

The introduction frames a foundational question about what data are sufficient to fully specify a CFT so that all correlation functions on arbitrary manifolds can, in principle, be computed. While operator spectra and OPE coefficients consistent with bootstrap crossing are commonly cited, the authors emphasize that these data can be insufficient—distinct CFTs may share them yet differ by extended operator/defect content, and bootstrap solutions may not determine physics on manifolds with nontrivial topology.

They explicitly state that the answer to this minimal-data question in general spacetime dimensions is not currently known and may not be unique, highlighting a broad and unresolved structural problem in CFT.