$κ$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries

Details $κ$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries $κ$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries

2003-01-09

arxiv.org/abs/hep-th/0301056v2

Mod.Phys.Lett. A18 (2003) 753-770

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 15 pages. The address of the author (V.D. L.) corrected and references are completed

Scientific paper

10.1142/S0217732303009873

We describe the classical $o(3,2)$ $r$-matrices as generating the quantum deformations of either D=3 conformal algebra with mass-like deformation parameters or D=4 $AdS$ algebra with dimensionless deformation parameters. We describe the quantization of classical $o(3,2)$ $r$-matrices via Drinfeld twist method which locates the deformation in the coalgebra sector. Further we obtain the quantum $o(3,2)$ algebra in a convenient Hopf algebra form by considering suitable deformation maps from classical to deformed $o(3,2)$ algebra basis. It appears that if we pass from $\kappa$-deformed D =3 conformal algebra basis to the deformed D=4 $AdS$ generators basis the role of dimensionfull parameter is taken over by the $AdS$ radius $R$. We provide also the bilinear $o(3,2)$ Casimir which we express using the deformed D=3 conformal basis.

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