Counting Supershort Supermultiplets

TL;DR

This paper investigates the phenomenon of multiplet shortening for BPS solitons in N=1 two-dimensional models, introducing a new index related to the Dirac operator to count such short multiplets and exploring its implications.

Contribution

It introduces a novel index for counting supershort multiplets in hybrid models with nonflat target space metrics, extending previous Landau-Ginzburg analyses.

Findings

The new index is related to the Dirac operator on the soliton moduli space.

Most cases show the index vanishes, indicating no shortening occurs.

The central charge anomaly is generalized to include target space metric effects.

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. 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.