Higher-spin initial data in twistor space with complex stargenvalues

Abstract

This paper is a supplement to and extension of arXiv:1903.01399. In the internal twistor space of the 4D Vasiliev's higher-spin gravity, we study the star-product eigenfunctions of number operators with generic complex eigenvalues. In particular, we focus on a set of eigenfunctions represented by formulas with generalized Laguerre functions. This set of eigenfunctions can be written as linear combinations of two subsets of eigenfunctions, one of which is closed under the star-multiplication with the creation operator to a generic complex power -- and the other similarly with the annihilation operator. The two subsets intersect when the left and the right eigenvalues differ by an integer. We further investigate how star-multiplications with both the creation and annihilation operators together may change such eigenfunctions and briefly discuss some problems that we are facing in order to use these eigenfunctions as the initial data to construct solutions to Vasiliev's equations.

16 pages, 3 figures; v4: Section 5 revised and other minor modifications; published on JHEP

References in corpus (7)

• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• BTZ Black Hole as Solution of 3d Higher Spin Gauge Theory
• New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
• On Classical Solutions of 4d Supersymmetric Higher Spin Theory
• An axial gauge ansatz for higher spin theories