6d conformal gravity

TL;DR

This paper develops a gauge-invariant, ordinary-derivative formulation of six-dimensional conformal gravity, deriving a higher-derivative Lagrangian with quadratic and cubic curvature terms that aligns with known Weyl invariants.

Contribution

It introduces a novel ordinary-derivative approach for 6d conformal gravity, including auxiliary and Stueckelberg fields, and derives the corresponding higher-derivative Lagrangian.

Findings

Derived gauge-invariant Lagrangian with auxiliary fields.

Obtained higher-derivative 6d conformal gravity Lagrangian.

Connected the formulation to known Weyl invariants.

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.