Spin-locality of higher-spin theories and star-product functional classes

Abstract

Abstract The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the β → −∞ limiting shifted homotopy proposed recently in [1] where all ω2C2 higher-spin vertices were shown to be spin-local. For the β → −∞ limiting shifted contracting homotopy we identify the class of functions $$ {\mathcal{H}}^{+0} $$ 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 [2] to the β-shifted contracting homotopy and the relation underlying locality of the ω2C2 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 con- stituent fields ϕ and their local currents J(ϕ) 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.