Abstract
Large N factorization ensures that, for low-dimension gauge-invariant operators in the half-BPS sector of \( \mathcal{N}=4 \) SYM, products of holomorphic traces have vanishing correlators with single anti-holomorphic traces. This vanishing is necessary to consistently map trace operators in the CFT4 to a Fock space of graviton oscillations in the dual AdS5. 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.
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Garner, D., Ramgoolam, S. & Wen, C. Thresholds of large N factorization in CFT4: exploring bulk spacetime in AdS5 . J. High Energ. Phys. 2014, 76 (2014). https://doi.org/10.1007/JHEP11(2014)076
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DOI: https://doi.org/10.1007/JHEP11(2014)076