Abstract
We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.
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Acknowledgments
A.P. is grateful for support provided by the National Science and Engineering Council of Canada and the Fonds de Recherche du Québec — Nature et Technologies. A.P. is also supported by the Simons Investigator Award #376208 of A. Volovich. S.C.H.’s work is supported in parts by the National Science and Engineering Council of Canada (NSERC) and by the Canada Research Chair program, reference number CRC-2022-00421. S.C.H.’s work is additionally supported by a Simons Fellowships in Theoretical Physics (reference 905744) and by the Simons Collaboration on the non-perturbative Bootstrap. Z.Z. is funded by Fonds de Recherche du Québec — Nature et Technologies, and the Simons Foundation through the Simons Collaboration on the non-perturbative Bootstrap. 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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Caron-Huot, S., Pokraka, A. & Zahraee, Z. Two-point sum-rules in three-dimensional Yang-Mills theory. J. High Energ. Phys. 2024, 195 (2024). https://doi.org/10.1007/JHEP01(2024)195
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DOI: https://doi.org/10.1007/JHEP01(2024)195