Thresholds of large N factorization in CFT4 : Exploring bulk locality

Large N factorization ensures that, for low-dimension gauge-invariant operators in the half-BPS sector of N = 4 SYM, products of holomorphic traces have vanishing correlators with single anti-holomorphic traces. This is important in mapping these operators to states in the dual AdS5, with a Fock space structure of gravitons based on trace structures in CFT4. We investigate the factorization thresholds where the vanishing correlators become order one in the large N limit. Using the UV/IR relation, we can map the operator dimensions to the radial AdS positions of the gravitons, and interpret the factorization threshold as giving information on the limitations of bulk locality in quantum gravity in AdS. Quite generally, we find the threshold to be when the product of the two holomorphic operator dimensions is of order N logN. Our discussion includes non-extremal correlators and LLM backgrounds, and we observe intriguing similarities between the the energy-dependent running coupling of non-abelian gauge theories and some of our threshold equations