Establish the existence of suitable four-dimensional conformal field theories

Establish whether four-dimensional conformal field theories with the operator spectrum, sparse dynamics, large-N behavior, and supersymmetric tumbling properties required by the Super-Composite Higgs framework actually exist.

Background

The effective description assumes a quasi-conformal supersymmetric sector with suitable low-dimension operators, a controlled operator spectrum, and dynamics that can generate separated thresholds. Holographic Randall–Sundrum models provide calculable analogues, but they do not prove the existence of corresponding four-dimensional conformal theories.

The paper highlights two unresolved theoretical issues: whether complete conformal field theories densely populate the space suggested by holographic constructions and whether the sparse spectra required for weakly coupled five-dimensional duals can be realized in four dimensions. These questions concern the ultraviolet existence and completion of the assumed strong sector.