A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations

Abstract

In Vasiliev's unfolded formulation of higher-spin dynamics the standard fields are embedded on-shell into covariantly constant master fields valued in Lorentz-covariant slices of the star-product algebra A of functions on the singleton phase space. Correspondingly, the harmonic expansion is taken over compact slices of A that are unitarizable in a rescaled trace-norm rather than the standard Killing norm. Motivated by the higher-derivative nature of the theory, we examine indecomposable unitarizable Harish-Chandra modules consisting of standard massless particles plus linearized runaway solutions. This extension arises naturally in the above fiber approach upon realizing compact-weight states as non-polynomial analytic functions in A.

80 pages, 2 figures. Minor changes: typos corrected, two footnotes and references added. To be published in JHEP

References in corpus (6)

• Consistent couplings between spin-2 and spin-3 massless fields
• On Higher Spins with a Strong Sp(2,R) Condition
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• Shadows, currents and AdS fields
• (A)dS exchanges and partially-massless higher spins
• Higher-spin Chern-Simons theories in odd dimensions

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