Abstract
We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model appear at special points on the boundary, along with an abundance of unknown models hinting at a non conventional UV behaviour. We extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for the stress-energy tensor and conserved O(N) currents. Sum rules allow us to put bounds on the central charges of the conformal field theory (CFT) in the UV. We find that a big portion of the boundary can only flow from CFTs with infinite central charges. We track this result down to a particular behaviour of the amplitudes in physical kinematics and discuss its physical implications.
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Acknowledgments
We would like to thank Nima Afkhami-Jeddi, Victor Gorbenko, Kelian Haring, Yifei He, Andrea Manenti, Nafiz Ishtiaque, Denis Karateev, Shota Komatsu, Nat Levine, Joao Penedones, Aninda Sinha, Emilio Trevisani, Pedro Vieira, Xi Yin and Bernardo Zan for useful discussions. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at UPPMAX (Rackham) partially funded by the Swedish Research Council through grant agreement no. 2022-06725. Nordita is partially supported by Nordforsk. AG is also supported by a Royal Society funding, URF\R\221015. AV 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. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 949077).
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Córdova, L., Correia, M., Georgoudis, A. et al. The O(N) monolith reloaded: sum rules and Form Factor Bootstrap. J. High Energ. Phys. 2024, 93 (2024). https://doi.org/10.1007/JHEP01(2024)093
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DOI: https://doi.org/10.1007/JHEP01(2024)093