Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-06
Helv.Phys.Acta 67 (1994) 930-953
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, latex, PAR/LPTHE/94-10
Scientific paper
In order to study in a regularisation free manner the renormalisability of d=2 supersymmetric non-linear $\si$ models, one has to use the algebraic BRS methods ; moreover, in the absence of an off-shell formulation, one has often to deal with open algebras. We then recall in a pedagogical and non technical manner the standard methods used to handle these questions and illustrate them on N=1 supersymmetric non-linear $\si$ model in component fields, giving the first rigorous proof of their renormalisability. In the special case of compact homogeneous manifolds (non-linear $\si$ model on a coset space G/H), we obtain the supersymmetric extension of the analysis done some years ago in the bosonic case. A further publication will be devoted to extended supersymmetry.
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