Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

Abstract

We first prove that, in Vasiliev's theory, the zero-form charges studied in 1103.2360 and 1208.3880 are twisted open Wilson lines in the noncommutative $Z$ space. This is shown by mapping Vasiliev's higher-spin model on noncommutative Yang--Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higher-spin invariants given by the leading order of these $n$-point zero-form charges are equal to corresponding cyclically-invariant building blocks of $n$-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of 1210.7963 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of $n$ conserved currents in arbitrary dimension $d>2$, using polarization vectors, which is an original result. It is shown to agree, for $d=3$, with the results obtained in 1301.3123 in various dimensions and where polarization spinors were used.

arXiv comment1+42 pages, no figure

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• Higher-Spin Gauge Theories and Bulk Locality
• Light-Front Bootstrap for Chern-Simons Matter Theories
• More on Quantum Chiral Higher Spin Gravity
• One-loop Finiteness of Chiral Higher Spin Gravity
• Formal Higher Spin Gravities
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Higher spin fluctuations on spinless 4D BTZ black hole
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• Reconstructing the boundary of AdS from an infrared defect