Irreversibility and higher-spinconformal field theory

Abstract

I discuss theproperties of the central charges c and a forhigher-derivativeand higher-spin theories (spin 2 included). Ordinarygravity does not admit a straightforward identificationof c and a in the trace anomaly, because it is notconformal.On the other hand, higher-derivative theories can be conformal, buthave negative c and a.A third possibility is to considerhigher-spin conformal field theories.They are not unitary, but have a variety of interesting properties.Bosonic conformal tensors have apositive-definite action, equal to the square of a field strength, and ahigher-derivative gauge invariance. Thereexists 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 theoperator-product structure. Higher-spinconformal spinors have no gauge invariance, admita standard definition of c and a andcan be coupled to Abelian and non-Abelian gauge fields in a renormalizableway. At the quantum level, they contribute to the one-loop beta functionwith the same sign as ordinary matter, admit a conformal window andnon-trivial interacting fixed points. There are composite operators of highspin 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 thatfundamental quantum field theories should be renormalization-group(RG) interpolations between ultraviolet and infrared conformal fixedpoints,and quantum irreversibility should be ageneral principle of nature.