@article{958e9381a2094de997b5492ad982dfaf,
title = "The unitary supermultiplets of d = 3 anti-de Sitter and d = 2 conformal superalgebras",
abstract = "We classify the d = 3 anti-de Sitter and d = 2 conformal superalgebras and give a general construction of their positive energy unitary representations. The corresponding supergroups are in general direct products G1 × G2 of two simple supergroups G1 and G2. We study in detail the cases when G1 (and/or G2) is SU(1,1/N) or Osp(2M/2, R).",
author = "M. G{\"u}naydin and G. Sierra and Townsend, {P. K.}",
note = "Funding Information: Ground states of supergravity theories that preserve supersymmetry have a supergroup as their manifest invariance group, i.e. particle states belong to unitary supermultiplets of this supergroup. The supergroups of relevance in this context have been classified by Nahm \[1\].T he anti-de Sitter supergroups, in particular, have attracted considerable interest in recent years. These are supersymmetric generalizations of the anti-de Sitter groups SO(d-1,2) of (d-1) + 1 = d space-time dimensions. Simple anti-de Sitter (ADS) supergroups exist only for d = 2, 4, 5, 6 and 7. Observe that d = 3 is not represented in this list, despite the fact that there does exist a d = 3 supergravity theory with a supersymmetric (ADS3) background \[2\].T he reason is that the AdS 3 group SO(2,2) is not simple, but is in fact locally the * This work was supported in part by the US Department of Energy under contract W-7405-ENG-48 and the Director, Office of Energy Research, Division of High Energy Physics of the US Department of Energy under contract DE-AC03-76-SFO-0098. ** Participating guest.",
year = "1986",
month = sep,
day = "15",
doi = "10.1016/0550-3213(86)90293-2",
language = "English (US)",
volume = "274",
pages = "429--447",
journal = "Nuclear Physics, Section B",
issn = "0550-3213",
publisher = "Elsevier B.V.",
number = "2",
}