Abstract
Analysis of the first-order corrections to higher-spin equations is extended to homotopy operators involving shift parameters with respect to the spinor Y variables, the argument of the higher-spin connection ω(Y) and the argument of the higher-spin zero-form C(Y). It is shown that a relaxed uniform (y + p)-shift and a shift by the argument of ω(Y) respect the proper form of the free higher-spin equations and constitute a one-parametric class of vertices that contains those resulting from the conventional (no shift) homotopy. A pure shift by the argument of ω(Y) is shown not to affect the one-form higher-spin field W in the first order and, hence, the form of the respective vertices.
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Tarusov, A.A., Ushakov, K.A. & Vasiliev, M.A. Shifted homotopy analysis of the linearized higher-spin equations in arbitrary higher-spin background. J. High Energ. Phys. 2023, 128 (2023). https://doi.org/10.1007/JHEP03(2023)128
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DOI: https://doi.org/10.1007/JHEP03(2023)128