  Covariant (Lorentz invariant) fracton matter, minimally coupled and charged
under a symmetric rank two gauge tensor, is considered. The gauge
transformations correspond to linearised longitudinal diffeomorphisms.
Consistent anomalies are computed using the BRST cohomological method. They
depend only on the gauge field, treated as a background field, and on the gauge
parameter, promoted to an anticommuting scalar ghost field. The problem is
phrased in terms of polyforms, whose total degree is the sum of the form degree
and of the ghost number. The most general anomaly in two dimensions and in four
dimensions is computed and an anomaly in arbitrary dimension is individuated.
In conclusion, it is shown that a simple higher-derivative scalar field theory
is an example of covariant fracton matter. The model enjoys a global symmetry,
which can be anomalous.
