Bezoutian Decoupling for Conformal Yang–Mills Multiplets in (A)dS

Abstract

Metsaev's formulation of conformal Yang–Mills theory in six, eight, and ten dimensions admits a change of variables from a generic auxiliary-field presentation to a direct sum of massless and massive Stueckelberg systems. The proposed matrices in arbitrary even dimension were left conjectural. Writing d for one less than the spacetime dimension, we prove the vector and radical diagonalization identities for every D=d+1=2N+4, N≥1. The generic kinetic form is the Bezout matrix of z∏_{i=1}^N(z−ρi(2N+1−i)) and 1; evaluation at its simple roots produces the Vandermonde congruence appearing in the field redefinition. The same calculation gives closed formulas for the inverse, determinant, and inertia, and identifies the normalization weights with Johnson-graph multiplicities. Any nonlinear coefficient algebra already specified in the generic formulation is transported by this change of basis. The result does not construct such an algebra in arbitrary dimension: at N=4, associativity, Frobenius invariance, and a fixed flat specialization still admit a one-parameter family of pairwise distinct products in a fixed generic basis.