On current contribution to Fronsdal equations

Abstract

We explore a local form of second-order Vasiliev equations proposed in [arXiv:1706.03718] and obtain an explicit expression for quadratic corrections to bosonic Fronsdal equations, generated by gauge-invariant higher-spin currents. Our analysis is performed for general phase factor, and for the case of parity-invariant theory we find the agreement with expressions for cubic vertices available in the literature. This provides an additional indication that field redefinition proposed in [arXiv:1706.03718] is the proper one.

arXiv comment15 pages. V3: typos corrected; references added; Introduction extended. To appear in Physics Letters B

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• Homotopy Operators and Locality Theorems in Higher-Spin Equations
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• Cosmological Shapes of Higher-Spin Gravity
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• On the Local Frame in Nonlinear Higher-Spin Equations
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• On holomorphic sector of higher-spin theory
• Cubic interaction vertices for massive/massless continuous-spin fields and arbitrary spin fields
• On one loop corrections in higher spin gravity
• On unfolded off-shell formulation for higher-spin theory
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• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
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• On the Fradkin-Vasiliev formalism in d=4
• Novel $\mathcal{N}=2$ higher-spin supercurrents