Abstract
We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large-N chiral perturbation theory (χPT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scale M using the primal method, thereby confirming the consistency of the large-N expansion. In the end, we translate the large-N χPT bounds to constrain the higher derivative corrections of holographic QCD models.
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Acknowledgments
We thank Simon Caron-Huot and Rohan Moola for their initial collaboration on the numerical exploration of the primal S-matrix bootstrap. We are also grateful to Jan Abert, Simon Caron-Huot, Miguel Correia, Julio Para-Martinez, David Simmons-Duffin, Zhuo-Hui Wang and Shuang-Yong Zhou for insightful discussions, and to Jan Abert for sharing their raw data, and to Simon Caron-Huot for valuable comments on the draft. Additionally, we would like to thank Ofer Aharony, Gabriel Cuomo, Leonardo Rastelli, Victor Rodriguez, Igor Klebanov, Juan Maldacena, and Pedro Vieira for useful conversations. YZL is supported in parts by the Simons Foundation through the Simons Collaboration on the Nonperturbative Bootstrap and by the US National Science Foundation under Grant No. PHY- 2209997. The computations presented here were partly conducted using the Narval and Graham clusters supported by Calcul Quèbec and Compute Canada, and partly conducted in the Resnick High Performance Computing Center, a facility supported by Resnick Sustainability Institute at the California Institute of Technology.
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Li, YZ. Effective field theory bootstrap, large-N χPT and holographic QCD. J. High Energ. Phys. 2024, 72 (2024). https://doi.org/10.1007/JHEP01(2024)072
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DOI: https://doi.org/10.1007/JHEP01(2024)072