Abstract
We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.
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Acknowledgments
The authors would like to thank Miguel Paulos for useful discussions and Manuel Loparco for pointing out a typo in the first version of this paper. MM would like to thank the organizers of the “Bootstrapping nature” conference held at the Galileo Galilei Institute in October 2022, where some important ideas for this project were first learnt. TS would like to thank the Swiss Study Foundation, the Geissbuhler Foundation and the Werner Siemens Foundation for their support during the completion of this project. JP is supported by the Simons Foundation grant 488649 (Simons Collaboration on the Nonperturbative Bootstrap) and the Swiss National Science Foundation through the project 200020_197160 and through the National Centre of Competence in Research SwissMAP. MM is supported by the SNSF Ambizione grant PZ00P2_193472.
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Meineri, M., Penedones, J. & Spirig, T. Renormalization group flows in AdS and the bootstrap program. J. High Energ. Phys. 2024, 229 (2024). https://doi.org/10.1007/JHEP07(2024)229
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DOI: https://doi.org/10.1007/JHEP07(2024)229