Theory of higher spin tensor currents and central charges

TL;DR

This paper develops a comprehensive framework for higher spin tensor currents in quantum field theory, analyzing their properties, operator product expansions, and central charges, with applications to conformal field theories and renormalization group flows.

Contribution

It introduces a detailed classification of higher spin currents, computes their central charges, and explores their behavior across RG trajectories, extending the understanding of conformal and off-critical theories.

Findings

Explicit one-loop calculations of higher spin central charges.

Classification of space-time invariants for higher spin currents.

Analysis of RG flows and phenomena like I-degeneracy removal.

Abstract

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 s between 0 and 5 (and a second label I) appear in 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 c_(s,I) 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 c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) 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 CFT's as a way to go beyond perturbation theory.