Abstract
The paper aims at the qualitative criterion of higher-spin locality. Perturbative analysis of the Vasiliev equations gives rise to the so-called z-dominated non-localities which nevertheless disappear from interaction vertices leaving the final result spin-local in all known cases. This has led one to the z-dominance conjecture that suggests universality of the observed cancellations. Here we specify conditions which include observation of the higher-spin shift symmetry and prove validity of this recently proposed conjecture. We also define a class of spin-local and shift-symmetric field redefinitions which is argued to be the admissible one with respect to spin-locality.
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Acknowledgments
We would like to thank Sasha Smirnov for fruitful discussions on several technical issues of our analysis. In particular, the speculation on analytic but not Lorentz invariant solutions of (8.8) was very stimulating. The authors are also grateful to O.A. Gelfond and M.A. Vasiliev for many valuable comments on the draft. This research was supported by the Russian Science Foundation grant 18-12-00507.
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Didenko, V.E., Korybut, A.V. On z-dominance, shift symmetry and spin locality in higher-spin theory. J. High Energ. Phys. 2023, 133 (2023). https://doi.org/10.1007/JHEP05(2023)133
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DOI: https://doi.org/10.1007/JHEP05(2023)133