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

Roberto Bonezzi, Nicolas Boulanger, David De Filippi, Per Sundell

Resultado de la investigación: Article

14 Citas (Scopus)

Resumen

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 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.

Idioma originalEnglish
Número de artículo475401
PublicaciónJournal of Physics A: Mathematical and Theoretical
Volumen50
N.º47
DOI
EstadoPublished - 1 nov 2017

Huella dactilar

Correlation Function
Conformal Field Theory
Building Blocks
Line
Polarization
Charge
Bilinear Operators
Invariant
Spinors
Zero Point
Spin Models
Yang-Mills Theory
polarization
Yang-Mills theory
Perturbation Theory
Three-dimension
High Energy
Mathematical operators
Gravity
Gravitation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Citar esto

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Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields. / Bonezzi, Roberto; Boulanger, Nicolas; De Filippi, David; Sundell, Per.

En: Journal of Physics A: Mathematical and Theoretical, Vol. 50, N.º 47, 475401, 01.11.2017.

Resultado de la investigación: Article

TY - JOUR

T1 - Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

AU - Bonezzi, Roberto

AU - Boulanger, Nicolas

AU - De Filippi, David

AU - Sundell, Per

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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 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.

AB - 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 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.

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