On conformal higher spins in curved background

Understand

We address the question of how to represent an interacting action for the tower of conformal higher spin fields in a form covariant with respect to a background metric.

• We use a background metric to define a star product which plays a central role in the definition of the corresponding gauge transformations.
• By an analogy with the kinetic term in the 4-derivative Weyl gravity action expanded near an on-shell background one expects that the kinetic term in such an action should be gauge-invariant in a Bach-flat metric.
• We demonstrate this fact to first order in expansion in powers of the curvature of the background metric.