Single State Supermultiplet in 1+1 Dimensions

Abstract

We consider multiplet shortening for BPS solitons in N=1 two-dimensional models. Examples of the single-state multiplets were established previously in N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the fermion parity $(-1{)}^F$ due to boundary effects. This implies the disappearance of the boson-fermion classification resulting in abnormal statistics. We discuss an appropriate index that counts such short multiplets. A broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space is considered. Our index turns out to be related to the index of the Dirac operator on the soliton reduced moduli space (the moduli space is reduced by factoring out the translational modulus). The index vanishes in most cases implying the absence of shortening. In particular, it vanishes when there are only two critical points on the compact target space and the reduced moduli space has nonvanishing dimension. We also generalize the anomaly in the central charge to take into account the target space metric.

LaTex, 42 pages, no figures. Contribution to the Michael Marinov Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds. M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The paper is drastically revised compared to the first version. We add sections treating the following issues: (i) a new index counting one-state supermultiplets; (ii) analysis of hybrid models of general type; (iii) generalization of the anomaly in the central charge accounting for the target space metric

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