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

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 ${\varphi }^4$ scalar field vertex.

arXiv commentSection 3 extended, clarifications and references added, typos corrected; matches the published version

References in corpus (16)

• AdS Dual of the Critical O(N) Vector Model
• Massless Higher Spins and Holography
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Higher-Spin Gauge Theories and Bulk Locality
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• Chern-Simons Matter Theories and Higher Spin Gravity
• Homotopy Operators and Locality Theorems in Higher-Spin Equations
• On the Local Frame in Nonlinear Higher-Spin Equations
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes
• Test of the local form of higher-spin equations via AdS/CFT
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• Higher spin fluctuations on spinless 4D BTZ black hole

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• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• On $z$-dominance, shift symmetry and spin locality in higher-spin theory
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background