Counting Supershort Supermultiplets

Details Counting Supershort Supermultiplets Counting Supershort Supermultiplets

2001-08-22

arxiv.org/abs/hep-th/0108153v2

Phys.Lett. B522 (2001) 327-334

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTex; minor changes, references added

Scientific paper

10.1016/S0370-2693(01)01293-X

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. To count such short multiplets we introduce a new index. We consider the phenomenon of shortening in a broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space. Our index turns out to be related to the index of the Dirac operator on the soliton moduli space. The latter vanishes in most cases implying the absence of shortening. We also generalize the anomaly in the central charge to take into account the target space metric.

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