Abstract
In this second installment of a series of two papers on the \( \frac{1}{2} \)-BPS Wilson line defect CFT in \( \mathcal{N} \) = 4 super Yang-Mills, we focus on dynamical aspects of the theory, in particular studying four-point functions with analytic bootstrap methods. Relying on the results of [1] for the kinematics and strong coupling spectrum, we consider various four-point functions in the planar limit, in an expansion for large ’t Hooft coupling. Our ultimate goal is to provide a detailed derivation of the four-point function of the displacement supermultiplet at three loops, first presented in [2]. Along the way, we present a large amount of new results including four-point functions with zero, one or two long external supermultiplets. The last two represent a novelty in the analytic bootstrap literature and are instrumental in addressing the problem of operators degeneracy. Such phenomenon leads to the necessity of resolving a mixing problem that is more complicated than those usually encountered in the study of holographic correlators, thus leading us to the development of a new approach that we believe will have a wider range of applicability. Related to this issue, we analyze in some detail the structure of the dilatation operator in this model. Some of the ingredients that we use apply more generally to holographic theories, although a thorough investigation of these aspects is missing, to the best of our knowledge, in most interesting cases.
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Acknowledgments
We thank Fernando Alday and Pedro Liendo for collaboration at early stages of this work and for many fruitful discussions. We thank Fernando Alday for sharing with us unpublished notes and are grateful to Alex Gimenez-Grau and Johan Henriksson for sharing with us some Mathematica code and some unpublished results respectively. P.F. would like to thank Leonardo Rastelli, Gabriel Cuomo and Adar Sharon for useful discussions. The work of C.M. has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska Curie grant agreement No 754496. The work of P.F. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 787185).
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Ferrero, P., Meneghelli, C. Unmixing the Wilson line defect CFT. Part II. Analytic bootstrap. J. High Energ. Phys. 2024, 10 (2024). https://doi.org/10.1007/JHEP06(2024)010
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DOI: https://doi.org/10.1007/JHEP06(2024)010