Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-07-18
Eur.Phys.J.C21:735-747,2001
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 31 pages
Scientific paper
10.1007/s100520100769
Using recent results on string 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-Poincar\'e algebra obtained by Rausch de Traubenberg and Slupinsky, refs [1] and [29]. 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 $AdS_3$. The two so(1,2) Lorentz modules of spin $\pm{1\over k}$ used in building of the generalisation of the (1+2) Poincar\'e algebra are re-interpreted in our analysis as highest weight representations of the left and right Virasoro symmetries on the boundary of $AdS_3$. 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 generalise the so(1,2) result to higher rank lie algebras g.
Benkaddour Ilham
Rhalami Aziz El
Saidi El Hassan
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