Eur. Phys. J. C 21, 735-747 (2001)
Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of AdS3I. 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 , 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 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