An action principle for Vasiliev's four-dimensional higher spin gravity

Nicolas Boulanger, Per Sundell

Resultado de la investigación: Article

54 Citas (Scopus)

Resumen

We provide Vasilievs fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle. We first extend Vasilievs original system with differential forms in degrees higher than 1. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: one, a set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and the other, a set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of rank 2 or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on-shell, to Vasilievs original system.

Idioma originalEnglish
Número de artículo495402
PublicaciónJournal of Physics A: Mathematical and Theoretical
Volumen44
N.º49
DOI
EstadoPublished - 9 dic 2011

Huella dactilar

variational principles
Gages
Hamiltonians
Gravity
Gravitation
equations of motion
High-dimensional
gravitation
Duality
Lagrange multipliers
Equations of motion
Extended Systems
gauge invariance
Variational Principle
nonlinear equations
Equations of Motion
Shell
coding
curvature
interactions

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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An action principle for Vasiliev's four-dimensional higher spin gravity. / Boulanger, Nicolas; Sundell, Per.

En: Journal of Physics A: Mathematical and Theoretical, Vol. 44, N.º 49, 495402, 09.12.2011.

Resultado de la investigación: Article

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AU - Sundell, Per

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AB - We provide Vasilievs fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle. We first extend Vasilievs original system with differential forms in degrees higher than 1. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: one, a set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and the other, a set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of rank 2 or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on-shell, to Vasilievs original system.

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