  Area metrics are an intriguing generalization of length metrics which appears
in several quantum-gravity approaches. We describe the space of
diffeomorphism-invariant area-metric actions quadratic in fluctuations and
derivatives. A general theory is found to be specified by four parameters, two
of which are mass parameters for the non-length degrees of freedom. We find
that a two-parameter subclass of theories exhibits an additional shift symmetry
of the kinetic term, and leads to a ghost-free graviton propagator for the
effective theory obtained after integrating out the non-length degrees of
freedom. One of the two parameters determines the strength of parity
violations, the other defines a mass parameter for the non-length degrees of
freedom. The same type of action has been found to appear from modified
Plebanski theory and in the continuum limit of (effective) spin foams.
  We moreover find that area-metric actions in Lorentzian (but not in
Euclidean) signature feature wrong-sign kinetic and mass terms for the
non-length degrees of freedom. Nevertheless, despite a coupling of these
degrees of freedom to the length metric, the linearized dynamics turns out to
be stable for the above subclass of actions.
