6d conformal gravity

Abstract: In the framework of ordinary-derivative approach, conformal gravity in space-time of dimension six is studied. The field content, in addition to conformal graviton field, includes two auxiliary rank-2 symmetric tensor fields, two Stueckelberg vector fields and one Stueckelberg scalar field. Gauge invariant Lagrangian with conventional kinetic terms and the corresponding gauge transformations are obtained. One of the rank-2 tensor fields and the scalar field have canonical conformal dimension. With respect to these fields, the Lagrangian contains, in addition to other terms, a cubic potential. Gauging away the Stueckelberg fields and excluding the auxiliary fields via equations of motion, the higher-derivative Lagrangian of 6d conformal gravity is obtained. The higher derivative Lagrangian involves quadratic and cubic curvature terms. This higher-derivative Lagrangian coincides with the simplest Weyl invariant density discussed in the earlier literature. Generalization of de Donder gauge conditions to 6d conformal fields is also obtained.