Theory of higher spin tensor currents and central charges

We study higher spin tensor currents in quantum field theory. Scalar, spino r and vector fields admit unique "improved" currents of arbitrary spin, tra celess and conserved. Off criticality as well as at interacting fixed point s conservation is violated and the dimension of the current is anomalous. I n particular, currents T-(s,T-I) with spin 0 less than or equal to s less t han or equal to 5 (and a second label I) appear in the singular part of the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-tim e structure are classified. The result is used to write and discuss the mos t general OPE for interacting conformal held theories and off criticality. Higher spin central charges c(s)(l) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpo lating between the UV and IR limits are constructed. We compute the one-loo p values of all c(s)(l) and investigate the RG trajectories of quantum fiel d theories in the conformal window following our approach. In particular, w e discuss certain phenomena (perturbative and non-perturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy. Finally , we address the problem of formulating an action principle for the RG traj ectory connecting pairs of CFT4's as a way to go beyond perturbation theory . (C) 1999 Elsevier Science B.V.