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On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry

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arxiv hep-th/0209056 v2 pith:OPXXYDKZ submitted 2002-09-06 hep-th

F.A. Dolan , H. Osborn This is my paper
classification hep-th
keywords semi-shortshortdimensionfourmultipletmultipletsprimaryrepresentations
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Possible short and semi-short representations for $\N=2$ and $\N=4$ superconformal symmetry in four dimensions are discussed. For $\N=4$ the well known short supermultiplets whose lowest dimension conformal primary operators correspond to $\half$-BPS or ${1\over 4}$-BPS states and are scalar fields belonging to the $SU(4)_r$ symmetry representations $[0,p,0]$ and $[q,p,q]$ and having scale dimension $\Delta =p$ and $\Delta = 2q+p$ respectively are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For $\N=4$ a ${1\over 4}$-BPS multiplet need not have a protected dimension unless the primary state belongs to a $[1,p,1]$ representation.

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Cited by 4 Pith papers

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