TY - JOUR

T1 - Gravitational and gauge couplings in Chern-Simons fractional spin gravity

AU - Boulanger, Nicolas

AU - Sundell, Per

AU - Valenzuela, Mauricio

N1 - Funding Information:
We thank Thomas Basile, Xavier Bekaert, Fabien Buisseret, Slava Didenko, Dileep Jatkar, Antal Jevicki and Tomas Prochazka for discussions. For are especially grateful to Thomas Basile for collaboration in proving the relation (3.40). N.B. is supported by the ARC contract No AUWB-2010-10/15-UMONS-1. P.S. is supported by Fondecyt Regular grant No 1140296 and Conicyt grant DPI 20140115. M.V. acknowledges the hospitality of UNAB (Santiago) and CECs (Valdivia).

PY - 2016/1/1

Y1 - 2016/1/1

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.

KW - Anyons

KW - Chern-Simons Theories

KW - Higher Spin Symmetry

UR - http://www.scopus.com/inward/record.url?scp=85000405763&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2016)173

DO - 10.1007/JHEP01(2016)173

M3 - Article

AN - SCOPUS:85000405763

VL - 2016

SP - 1

EP - 28

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 173

ER -