Elsevier

Nuclear Physics B

Volume 168, Issue 2, 9 June 1980, Pages 354-364
Nuclear Physics B

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

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Abstract

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CPN−1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CPN−1 model thus obtained admits an O(2) extended supersymmetry.

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