Theory of higher spin tensor currents and central charges Original Research Article

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique “improved” currents of arbitrary spin, traceless and conserved. Off criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents J(s,I) with spin 0 ⩽ s ⩽ 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-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off criticality. Higher spin central charges csI with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all csI and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we 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 trajectory connecting pairs of CFT4ʹs as a way to go beyond perturbation theory.