2017/05/31 by Roberto Bonezzi, Nicolas Boulanger, David De Filippi +1 · 19 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Computation #Conformal field theory #Conformal map #Free field #Integrable system #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Polarization (electrochemistry) #Spinor #hep-th
paper · pdf · doi:10.1088/1751-8121/aa8efa
published in Journal of Physics A Mathematical and Theoretical 50(47), 475401 (Institute of Physics) · 1+42 pages, no figure
openalex created_date 2017/05/19 · openalex publication_date 2017/09/26 · arxiv created 2017/12/18 · arxiv updated 2017/12/19 · openalex updated_date 2026/08/05
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>d</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> <mml:mspace width="thinmathspace"/> </mml:mstyle> </mml:math> using polarization vectors, which is an original result. It is shown to agree, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mspace width="thinmathspace"/> </mml:mstyle> </mml:math> , 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.