Spin-Locality of $\eta^2$ and $\bar\eta^2$ Quartic Higher-Spin Vertices

V. E. Didenko; O. A. Gelfond; A. V. Korybut; M. A. Vasiliev

doi:10.1007/jhep12(2020)184

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arXiv · 2009.02811

Spin-Locality of $\eta^2$ and $\bar\eta^2$ Quartic Higher-Spin Vertices

V. E. Didenko·O. A. Gelfond·A. V. Korybut·M. A. Vasiliev

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Abstract

Higher-spin theory contains a complex coupling parameter $\eta$. Different higher-spin vertices are associated with different powers of $\eta$ and its complex conjugate $\bar \eta$. Using $Z$-dominance Lemma, that controls spin-locality of the higher-spin equations, we show that the third-order contribution to the zero-form $B(Z;Y;K)$ admits a $Z$-dominated form that leads to spin-local vertices in the $\eta^2$ and $\bar \eta^2$ sectors of the higher-spin equations. These vertices include, in particular, the $\eta^2$ and $\bar \eta^2$ parts of the $\phi^4$ scalar field vertex.

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V. E. Didenko, O. A. Gelfond, A. V. Korybut, M. A. Vasiliev. 2020-09-06. Spin-Locality of $\eta^2$ and $\bar\eta^2$ Quartic Higher-Spin Vertices. https://doi.org/10.1007/jhep12(2020)184

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