Abstract
We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension unprotected operator in \( \mathcal{N} \) = 4 SU(N) super-Yang-Mills theory for a wide range of N and Yang-Mills couplings gYM. We find that our bounds are approximately saturated by weak coupling results at small gYM. Furthermore, at large N our bounds interpolate between integrability results for the Konishi operator at small gYM and strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at large gYM. In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling.
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Acknowledgments
We thank Luis Fernando Alday, Tobias Hansen, and Julius Julius for useful discussions. SSP and RD are supported in part by the US NSF under Grant No. 2111977. SMC is supported by the Royal Society under the grant URF\R1\221310. RD was also supported in part by an NSF GRFP.
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Chester, S.M., Dempsey, R. & Pufu, S.S. Level repulsion in \( \mathcal{N} \) = 4 super-Yang-Mills via integrability, holography, and the bootstrap. J. High Energ. Phys. 2024, 59 (2024). https://doi.org/10.1007/JHEP07(2024)059
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DOI: https://doi.org/10.1007/JHEP07(2024)059