Abstract

with the minimal spin content (3=2;1) [1][2]. Here the importantpoint is that the vector-spinor has no spin 2 superpartner, but has only spin 1 counterpart.In other words, the system has only global supersymmetry, but no local supersymmetryor supergravity. One of the ultimate aims is to establish the foundation for more generalsupersymmetric higher-spin interactions [3].However, there have been so far no consistent interactions introduced for the (3=2;1) mul-tiplet, at least in terms of component elds. This situation is understandable through theconventional wisdom that once spin 3/2 is introduced, there should be spin 2 graviton, re-sulting necessarily in supergravity for consistency. Another technical reasons is that theauxiliary eld structure with o -shell super elds [1][2][4] is so involved that the correspond-ing formulations in component elds is impractically complicated. This is despite the factthat o -shell super eld formulation is powerful enough to present interaction lagrangians insuperspace.This problem appears to be easily solved in superspace. In superspace, the (3=2;1) mul-tiplet is represented by a spinor super eld and a real scalar super eld V [1][2][4]. Wecan conjecture, for example, a total action to be II

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