Gravitational and gauge couplings in Chern-Simons fractional spin gravity

Nicolas Boulanger, Per Sundell, Mauricio Valenzuela

Resultado de la investigación: Article

3 Citas (Scopus)

Resumen

Abstract: We propose an extension of Vasiliev’s supertrace operation for the enveloping algebra of Wigner’s deformed oscillator algebra to the fractional spin algebra given in arXiv:1312.5700. We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern-Simons theory for Blencowe-Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2ℓ + 1) or gl(ℓ|ℓ + 1) and various real forms thereof.

Idioma originalEnglish
Número de artículo173
Páginas (desde-hasta)1-28
Número de páginas28
PublicaciónJournal of High Energy Physics
Volumen2016
N.º1
DOI
EstadoPublished - 1 ene 2016

Huella dactilar

algebra
gravitation
projectors
integers
oscillators
operators
ground state

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Citar esto

Boulanger, Nicolas ; Sundell, Per ; Valenzuela, Mauricio. / Gravitational and gauge couplings in Chern-Simons fractional spin gravity. En: Journal of High Energy Physics. 2016 ; Vol. 2016, N.º 1. pp. 1-28.
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Gravitational and gauge couplings in Chern-Simons fractional spin gravity. / Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio.

En: Journal of High Energy Physics, Vol. 2016, N.º 1, 173, 01.01.2016, p. 1-28.

Resultado de la investigación: Article

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AU - Sundell, Per

AU - Valenzuela, Mauricio

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N2 - Abstract: We propose an extension of Vasiliev’s supertrace operation for the enveloping algebra of Wigner’s deformed oscillator algebra to the fractional spin algebra given in arXiv:1312.5700. We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern-Simons theory for Blencowe-Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2ℓ + 1) or gl(ℓ|ℓ + 1) and various real forms thereof.

AB - Abstract: We propose an extension of Vasiliev’s supertrace operation for the enveloping algebra of Wigner’s deformed oscillator algebra to the fractional spin algebra given in arXiv:1312.5700. We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern-Simons theory for Blencowe-Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2ℓ + 1) or gl(ℓ|ℓ + 1) and various real forms thereof.

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