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A note on three-point functions of conserved currents

Alexander Zhiboedov

Abstract

We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current conservation conditions. We present generating functionals for all structures in arbitrary d. In even dimensions we present an interpretation for each structure in terms of the corresponding free field. In odd dimensions d>3 an infinite number of structures is found which are not generated by known CFTs.

A note on three-point functions of conserved currents

Abstract

We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current conservation conditions. We present generating functionals for all structures in arbitrary d. In even dimensions we present an interpretation for each structure in terms of the corresponding free field. In odd dimensions d>3 an infinite number of structures is found which are not generated by known CFTs.

Paper Structure

This paper contains 17 sections, 40 equations.

Table of Contents

  1. Introduction
  2. Solution
  3. Interpretation
  4. $d=3$
  5. $d=4$
  6. Even $d>4$
  7. Odd $d>3$
  8. Case of one conserved current
  9. Three point function of stress tensors from the gravity dual
  10. Conclusions
  11. Appendix A
  12. Appendix B
  13. $j = 0$
  14. $j = {1 \over 2}$
  15. $j = 1$
  16. ...and 2 more sections