A conformally invariant Yang–Mills type energy and equation on 6-manifolds

We define a conformally invariant action S on gauge connections closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the connection. The Euler-Lagrange equations S, with respect to variation connection, provide higher-order analogue (source-free) Yang-Mills equations. For any connection A M, we S(A) by first defining Lagrangian density associated A. This not but has conformal transformation analogous Q-curvature. Integrating provides action. In special case that apply Cartan-tractor functional gradient recovers natural curvature called Fefferman-Graham obstruction tensor. So are exactly "obstruction-flat" condition for 6-manifolds. extends known results 4-dimensional manifolds where Bach tensor recovered