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} , 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.
Highlights
The most symmetric vacuum solution to nonlinear field equations for 4d massless fields of all spins of [3, 4] describes AdS4
For the β → −∞ limiting shifted contracting homotopy we identify the class of functions H+0, that do not contribute to the r.h.s. of HS field equations at a given order
Details of the derivation of the β-dependent shifted contracting homotopy are given in appendix B
Summary
The most symmetric vacuum solution to nonlinear field equations for 4d massless fields of all spins of [3, 4] describes AdS4. This will allow us to greatly simplify the formalism factoring out the structures that do not contribute to the final result In this setup, HS equations of [4] provide an extremely powerful tool for the analysis of HS gauge theories directly in the bulk with no reference to AdS/CF T allowing a systematic computation of higher-order HS vertices. It is shown here that the contribution resulting from q,−∞H2+0 is well defined in the limit β → −∞ but is pre-ultra-local that, in accordance with PLT, guarantees ultra-locality in the second order in HS zero-forms C. This implies that the part of the vertex bilinear in the zero-forms C is ultra-local. Details of the derivation of the β-dependent shifted contracting homotopy are given in appendix B
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