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

TL;DR

This paper introduces a fiber-based harmonic analysis method for unfolded higher-spin field equations, focusing on unitarizable modules and their analytic function representations within Vasiliev's framework.

Contribution

It presents a novel fiber approach to harmonic analysis in higher-spin theories, emphasizing unitarizable modules and non-polynomial analytic functions.

Findings

Identification of indecomposable unitarizable Harish-Chandra modules

Extension of the fiber approach to include runaway solutions

Representation of states as non-polynomial analytic functions

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.