Star-Product Functions in Higher-Spin Theory and Locality

Abstract

Properties of the functional classes of star-product elements associated with higher-spin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra $\mathcal{H}$, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.

arXiv comment25 pages; V2: The version to appear in JHEP, typos corrected, a comment in Section 6 added

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• Nonlinear higher spin theories in various dimensions
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• Static BPS black hole in 4d higher-spin gauge theory
• Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
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Cited by in corpus (7)

• On the Local Frame in Nonlinear Higher-Spin Equations
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Test of the local form of higher-spin equations via AdS/CFT
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Bulk quartic vertices from boundary four-point correlators
• On current contribution to Fronsdal equations
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory