Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background

Abstract

Analysis of the first-order corrections to higher-spin equations is extended to homotopy operators involving shift parameters with respect to the spinor $Y$ variables, the argument of the higher-spin connection $\omega (Y)$ and the argument of the higher-spin zero-form $C(Y)$. It is shown that a relaxed uniform $(y+p)$-shift and a shift by the argument of $\omega (Y)$ respect the proper form of the free higher-spin equations and constitute a one-parametric class of vertices that contains those resulting from the conventional (no shift) homotopy. A pure shift by the argument of $\omega (Y)$ is shown not to affect the one-form higher-spin field $W$ in the first order and, hence, the form of the respective vertices.

24 pages; V2: The analysis is extended to the homotopy shifts dependent on the argument of the higher-spin zero-form $C(Y)$. A relaxed uniform $(y+p)$-shift is shown to respect the free higher-spin equations in $Ad{S}_4$ the same time generating a one-parametric class of pairwise different interacting vertices. Acknowledgement added. Matches the published version

References in corpus (5)

• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes
• Spin-Locality of ${\eta }^2$ and ${\bar{\eta }}^2$ Quartic Higher-Spin Vertices
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$