Abstract
Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ, ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell.
The project was funded in part by F.R.S.-FNRS “Ulysse” Incentive Grant for Mobility in Scientific Research.
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14 March 2016
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP03(2016)076
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ArXiv ePrint: 1312.5700
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Boulanger, N., Sundell, P. & Valenzuela, M. Three-dimensional fractional-spin gravity. J. High Energ. Phys. 2014, 52 (2014). https://doi.org/10.1007/JHEP02(2014)052
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DOI: https://doi.org/10.1007/JHEP02(2014)052