Gravitational and gauge couplings in Chern-Simons fractional spin gravity

Nicolas Boulanger, Per Sundell, Mauricio Valenzuela

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number173
Pages (from-to)1-28
Number of pages28
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 1 Jan 2016


  • Anyons
  • Chern-Simons Theories
  • Higher Spin Symmetry

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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