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arXiv · 1312.5700

Three-dimensional fractional-spin gravity

Nicolas Boulanger·Per Sundell·Mauricio Valenzuela
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Abstract

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal non-abelian 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(N,N +/- 1) or gl(N|N +/- 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.

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Nicolas Boulanger, Per Sundell, Mauricio Valenzuela. 2014-02-10. Three-dimensional fractional-spin gravity. https://doi.org/10.1007/jhep02(2014)052

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