Thresholds of large N factorization in CFT 4 : exploring bulk spacetime in AdS 5

Large N factorization ensures that, for low-dimension gauge-invariant operators in the half-BPS sector of N = 4 $$ \mathcal{N}=4 $$ SYM, products of holomorphic traces have vanishing correlators with single anti-holomorphic traces. This vanishing is necessary to consistently map trace operators in the CFT 4 to a Fock space of graviton oscillations in the dual AdS 5 . We investigate the regimes at which the CFT correlators do not vanish but become of order one in the large N limit, which we call a factorization threshold . Quite generally, we find the threshold to be when the product of the two holomorphic operator dimensions is of order N log N . Our analysis considers extremal and non-extremal correlators and correlators in states dual to LLM backgrounds, and we observe intriguing similarities between the the energy-dependent running coupling of non-abelian gauge theories and our threshold equations. Finally, we discuss some interpretations of the threshold within the bulk AdS spacetime