Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Theory of higher spin tensor currents and central charges

D. Anselmi

TL;DR

Damiano Anselmi develops a comprehensive framework for higher spin tensor currents in four-dimensional quantum field theories, detailing how improved currents with spins up to $s=5$ arise and how their conservation is generically broken off criticality by anomalous dimensions $h_s$. Central to the program is the TT OPE, which classifies primary higher-spin channels and defines higher-spin central charges $c_s^{I}$ and central functions $c_{s,I}(g)$ that interpolate between UV and IR fixed points within the conformal window. The author provides explicit free-field constructions of the currents, their two-point functions, and the nonlocal projectors that isolate pure spin-$s$ contributions, then extends the TT OPE to interacting CFTs and off-critical theories, computing one-loop values of the central charges and exploring RG trajectories and degeneracy lifting. The work lays groundwork for a potentially nonperturbative formulation of RG flows via an action principle and connects to SUSY, dualities, and AdS/CFT, signaling a rich structure of secondary central charges and operator mixing in four-dimensional CFTs. Overall, the paper offers a detailed, technically rich blueprint for analyzing higher-spin sectors as probes of conformal dynamics and RG irreversibility.

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.

Theory of higher spin tensor currents and central charges

TL;DR

Damiano Anselmi develops a comprehensive framework for higher spin tensor currents in four-dimensional quantum field theories, detailing how improved currents with spins up to arise and how their conservation is generically broken off criticality by anomalous dimensions . Central to the program is the TT OPE, which classifies primary higher-spin channels and defines higher-spin central charges and central functions that interpolate between UV and IR fixed points within the conformal window. The author provides explicit free-field constructions of the currents, their two-point functions, and the nonlocal projectors that isolate pure spin- contributions, then extends the TT OPE to interacting CFTs and off-critical theories, computing one-loop values of the central charges and exploring RG trajectories and degeneracy lifting. The work lays groundwork for a potentially nonperturbative formulation of RG flows via an action principle and connects to SUSY, dualities, and AdS/CFT, signaling a rich structure of secondary central charges and operator mixing in four-dimensional CFTs. Overall, the paper offers a detailed, technically rich blueprint for analyzing higher-spin sectors as probes of conformal dynamics and RG irreversibility.

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.

Paper Structure

This paper contains 19 sections, 127 equations, 2 figures.

Table of Contents

  1. Introduction and motivation.
  2. Higher spin tensor currents and their two-point functions.
  3. Orthonormality.
  4. Spin 3.
  5. Spin 4.
  6. Spin 5.
  7. Critical and off-critical properties.
  8. Renormalization group analysis.
  9. Trace anomaly and higher spin anomalies.
  10. Treatment of the $h$-violation.
  11. The $TT$ operator product expansion.
  12. Scalar field.
  13. Vector field.
  14. Spinor.
  15. Classical and quantum conformal algebras.
  16. ...and 4 more sections

Figures (2)

  • Figure 3: Construction of $c_{4}$.
  • Figure 4: Higher spin central charges from many-point functions of the stress tensor.