Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields. (1st November 2017)

• Record Type: Journal Article
• Authors: Bonezzi, Roberto; Boulanger, Nicolas; De Filippi, David; Sundell, Per
• Is Part Of: Journal of physics. Volume 50:Number 47(2017)
• Publication Date: 2017-11-01
• Subjects: higher-spin gauge theory -- conformal field theory -- non-commutative field theory; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa8efa
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We first prove that, in Vasiliev's theory, the zero-form charges studied in Sezgin E and Sundell P 2011 (arXiv:1103.2360 [hep-th]) and Colombo N and Sundell P 20 (arXiv:1208.3880 [hep-th]) 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 Didenko V and Skvortsov E 2013 J. High Energy Phys . JHEP04(2013)158 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 Gelfond O A and Vasiliev M A 2013 Nucl. Phys . B 876 871–917 in various dimensions and where polarization spinors were used.