Abstract
We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three-dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of SU(N) and O(N) global symmetry. In both cases, we obtain general bounds on operator dimensions. In the large-N limit our bounds show features in correspondence of the expected position of fermionic QED3 in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED3 at large-N, we manage to restrict the plane of certain operator dimensions to a small island, where QED3 must live.
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Acknowledgments
We would like to thank Marten Reehorst for participating in the early stages of this project. We also thank Francesco Russo, Francesco Bertucci, Emilio Trevisani for discussions and Stefanos Kousvos for discussions and comments on the manuscript. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 758903). The computations in this paper were run on the Symmetry cluster of Perimeter institute.
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He, YC., Rong, J., Su, N. et al. Non-Abelian currents bootstrap. J. High Energ. Phys. 2024, 175 (2024). https://doi.org/10.1007/JHEP03(2024)175
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DOI: https://doi.org/10.1007/JHEP03(2024)175