Noncommutative Wilson lines in higher-spin theory and correlators of free conformal fields

Abstract

In this note, we review the results of 1705.03928 on a special class of observables of Vasiliev’s four-dimensional higher spin gravity theory, referred to as zero-form charges. These objects were shown to be twisted open Wilson lines in the noncommutative twistor Z space. For boundary conditions corresponding to higher spin fields in asymptically anti-de Sitter spacetime, their classical perturbative expansion was then proven to start with cyclically-invariant building blocks of n-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the CFT side, the proof involves the explicit computation of the aforementioned building blocks in arbitrary dimension d > 2, which generalizes known results on 3-point functions for any d > 2, and on n-point functions for d = 3.