  Two-dimensional quantum fields in electric and gravitational backgrounds can
be described by conformal field theories, and hence all the physical
(covariant) quantities can be written in terms of the corresponding holomorphic
quantities. In this paper, we first derive relations between covariant and
holomorphic forms of higher-spin currents in these backgrounds, and then, by
using these relations, obtain higher-spin generalizations of the trace and
gauge (or gravitational) anomalies up to spin 4. These results are applied to
derive higher-moments of Hawking fluxes in black holes in a separate paper
arXiv:0710.0456.
