Can a nonunitary theory prove the irreversibility theorem?

Long-range quantum field theories break unitarity but still exhibit conformal symmetry at fixed points. The authors show that even without unitarity, the renormalization group flow obeys a strict gradient equation (the A-theorem structure) up to three-loop order, with the flow function matching the sphere free-energy from conformal field theory. This suggests irreversibility and a fundamental theorem can hold even when unitarity fails.