Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes

Abstract

The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the $\beta \to -\infty$ limiting shifted homotopy proposed recently in arXiv:1909.04876 where all ${\omega }^2{C}^2$ higher-spin vertices were shown to be spin-local. For the $\beta \to -\infty$ limiting shifted contracting homotopy we identify the class of functions ${\mathcal{H}}^{+0}$, that do not contribute to the r.h.s. of HS field equations at a given order. A number of theorems and relations that organize analysis of the higher-spin equations are derived including extension of the Pfaffian Locality Theorem of arXiv:1805.11941 to the $\beta$-shifted contracting homotopy and the relation underlying locality of the ${\omega }^2{C}^2$ sector of higher-spin equations. Space-time interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is space-time local in terms of original constituent fields $\Phi$ and their local currents $J(\Phi )$ of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.

51 pages, no figures; V2 minor corrections: typos fixed, clarifications and affiliation added; V3 55 pages, Section 3 extended to clarify the notions of spin-locality and ultra-locality. Matches the published version

References in corpus (2)

• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality

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