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Particles and Fields

Eur. Phys. J. C 21, 735-747 (2001)
DOI: 10.1007/s100520100769

Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of AdS3

I. Benkaddour, A. El Rhalami and E.H. Saidi

Lab/UFR High Energy Physics, Physics Department, Faculty of Science, Av. Ibn Battota, B.P. 1014, Rabat, Morocco

(Received: 20 July 2000 / Published online: 19 September 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )

Using recent results on strings on AdS $_3\times N^d$, where N is a d dimensional compact manifold, we re-examine the derivation of the non-trivial extension of the (1+2)-dimensional-Poincaré algebra obtained by Rausch de Traubenberg and Slupinsky. We show by explicit computation that this new extension is a special kind of fractional supersymmetric algebra which may be derived from the deformation of the conformal structure living on the boundary of AdS3. The two so(1,2) Lorentz modules of spin $\pm 1/
k$ used in building of the generalization of the (1+2) Poincaré algebra are re-interpreted in our analysis as highest weight representations of the left and right Virasoro symmetries on the boundary of AdS3. We also complete known results on 2d-fractional supersymmetry by using spectral flow of affine Kac-Moody and superconformal symmetries. Finally we make preliminary comments on the trick of introducing Fth roots of g-modules to generalize the so(1,2) result to higher rank Lie algebras g.

© Società Italiana di Fisica, Springer-Verlag 2001