Non Trivial Extension of the (1+2)-Poincaré Algebra and Conformal Invariance on the Boundary of $Ad{S}_3$

Abstract

Using recent results on string on $Ad{S}_3\times N^d$, 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, 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 $Ad{S}_3$. The two so(1,2) Lorentz modules of spin $\pm \frac{1}{k}$ used in building of the generalisation 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 $Ad{S}_3$. 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.

Latex, 31 pages

References in corpus (1)

• More Comments on String Theory on AdS_3

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