### Abstract

We continue our study of the unitary supermultiplets of the script N = 8 d = 5 anti-de Sitter (AdS_{5}) superalgebra SU(2, 2/4), which is the symmetry algebra of type IIB superstring theory on AdS_{5} × S^{5}. SU(2,2/4) is also the script N = 4 extended conformal superalgebra in d = 4. We show explicitly how to go from the compact SU(2) × SU(2) × U(1) basis to the non-compact SL(2, ℂ) × D basis of the positive (conformal) energy unitary representations of the conformal group SU(2, 2) in d = 4. The doubleton representations of the AdS_{5} group SU(2, 2), which do not have a smooth Poincaré limit in d = 5, are shown to represent fields with vanishing masses in four-dimensional Minkowski space, i.e. on the boundary of AdS_{5}, where SU(2, 2) acts as conformal group. The unique CPT self-conjugate irreducible doubleton supermultiplet of SU(2, 2/4) is simply the script N = 4 Yang-Mills supermultiplet in d = 4. We study some novel short non-doubleton supermultiplets of SU(2, 2/4) that have spin range 2 and that do not appear in the Kaluza-Klein spectrum of type IIB supergravity or in tensor products of the script N = 4 Yang-Mills supermultiplet with itself. These novel supermultiplets can be obtained from tensoring chiral doubleton supermultiplets,some of which we expect to be related to the massless limits of 1/4 BPS states. Hence, these novel supermultiplets may be relevant to the solitonic sector of IIB superstring and/or (p,q) superstrings over AdS_{5} × S^{5}.

Original language | English (US) |
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Pages (from-to) | 737-758 |

Number of pages | 22 |

Journal | Nuclear Physics B |

Volume | 544 |

Issue number | 3 |

DOIs | |

State | Published - Apr 12 1999 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

_{5}/CFT

_{4}duality.

*Nuclear Physics B*,

*544*(3), 737-758. https://doi.org/10.1016/S0550-3213(99)00007-3