Abstract
In this paper we revisit the general phenomenon that scattering amplitudes of pions can be obtained from “dimensional reduction” of gluons in higher dimensions in a more general context. We show that such “dimensional reduction” operations universally turn gluons into pions regardless of details of interactions: under such operations any amplitude that is gauge invariant and contains only local simple poles becomes one that satisfies Adler zero in the soft limit. As two such examples, we show that starting from gluon amplitudes in both superstring and bosonic string theories, the operations produce “stringy” completion of pion scattering amplitudes to all orders in α′, with leading order given by non-linear sigma model amplitudes. Via Kawai-Lewellen-Tye relations, they give closed-stringy completion for Born-Infeld theory and the special Galileon theory, which are directly related to gravity amplitudes in closed-string theories. We also discuss how they naturally produce stringy models for mixed amplitudes of pions and colored scalars.
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Acknowledgments
We are very grateful to Song He for proposing this problem. It is our pleasure to thank Qu Cao and Song He for collaborations on the early stage of this project and stimulating discussions. We also thank Canxin Shi, Yao-Qi Zhang and Yong Zhang for discussions and collaborations on related projects. This work is supported by the National Natural Science Foundation of China under Grant No. 12225510, 11935013, 12047503.
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Dong, J., Li, X. & Zhu, F. Pions from higher-dimensional gluons: general realizations and stringy models. J. High Energ. Phys. 2024, 149 (2024). https://doi.org/10.1007/JHEP07(2024)149
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DOI: https://doi.org/10.1007/JHEP07(2024)149