Irreversibility and higher-spin conformal field theory

I discuss the properties of the central charges c and a for higher-derivati ve and higher-spin theories (spin 2 included). Ordinary gravity does not ad mit a straightforward identification of c and a in the trace anomaly, becau se it is not conformal. On the other hand, higher-derivative theories can b e 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 vari ety of interesting properties. Bosonic conformal tensors have a positive-de finite action, equal to the square of a field strength, and a higher-deriva tive gauge invariance. There exists a conserved spin-2 current (not the can onical stress tensor) defining positive central charges c and a, I calculat e the values of c and a and study the operator-product structure. Higher-sp in 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 b eta function with the same sign as ordinary matter, admit a conformal windo w and non-trivial interacting fixed points. There are composite operators o f high spin and low dimension, which violate the Ferrara-Gatto-Grillo theor em. Finally, other theories, such as conformal antisymmetric tensors, exhib it more severe internal problems. This research is motivated by the idea th at 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.