Abstract
Properties of the functional classes of star-product elements associated with higher-pin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra $$ \mathrm{\mathscr{H}} $$ , where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.
Highlights
Where ρ is the AdS radius and D is the space-time covariant derivative
Higher perturbations lead to multiple homotopy integrals which are in the core of the analysis of star-product functional classes in the sequel
In agreement with the expectation of [1], this conjecture rules out the pseudolocal field redefinitions resulting from the integrating flow of [1]
Summary
HS equations were formulated in [1, 3, 4] in terms of the associative HS star product ∗ which acts on functions of two variables ZA and YA An important property of star product (2.1) is that it admits the inner Klein operator. The Klein operator ΥY for the star product of Z-independent functions, which amounts to the Weyl star product g)(Y dM U dM V exp [iU AV BCAB] f (Y + U )g(Y + V ) ,. From here it follows that though ΥY is well behaving with respect to the star product its supertrace is divergent str(ΥY ) = ∞ ∼ δM (0). Str(Υ) remains divergent as δ2M (0) in the HS star product. Str(f ) = ∞ for any f (Z; Y ) behaving in Y and Z like Υ This fact plays the key role in [7] where the supertrace of nontrivial invariant functionals is demanded to be divergent
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