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Higher-spin current multiplets in operator-product expansions

D. Anselmi

Abstract

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.

Higher-spin current multiplets in operator-product expansions

Abstract

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.

Paper Structure

This paper contains 11 sections, 103 equations.

Table of Contents

  1. Introduction
  2. Scalar field
  3. Fermion
  4. The simplest hierarchy: hypermultiplet
  5. Vector field and its generalization to arbitrary dimension
  6. The N=4 hierarchy
  7. The N=2 vector multiplet
  8. Formulas for projectors and conformal tensors
  9. Trace anomaly
  10. Complete form of the higher-spin currents
  11. Appendix: the $(n/2-1)$-form