  I discuss the properties of the central charges c and a for higher-derivative
and higher-spin theories (spin 2 included). Ordinary gravity does not admit a
straightforward identification of c and a in the trace anomaly, because it is
not conformal. On the other hand, higher-derivative theories can be conformal,
but have negative c and a. A third possibility is to consider higher-spin
conformal field theories. They are not unitary, but have a variety of
interesting properties. Bosonic conformal tensors have a positive-definite
action, equal to the square of a field strength, and a higher-derivative gauge
invariance. There exists a conserved spin-2 current (not the canonical stress
tensor) defining positive central charges c and a. I calculate the values of c
and a and study the operator-product structure. Higher-spin conformal spinors
have no gauge invariance, admit a standard definition of c and a and can be
coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the
quantum level, they contribute to the one-loop beta function with the same sign
as ordinary matter, admit a conformal window and non-trivial interacting fixed
points. There are composite operators of high spin and low dimension, which
violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as
conformal antisymmetric tensors, exhibit more severe internal problems. This
research is motivated by the idea that fundamental quantum field theories
should be renormalization-group (RG) interpolations between ultraviolet and
infrared conformal fixed points, and quantum irreversibility should be a
general principle of nature.
