Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-05-12
JHEP 0206 (2002) 040
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 35 pages, version appeared in JHEP
Scientific paper
10.1088/1126-6708/2002/06/040
The superconformal structure of coset superspaces with AdS_m x S^n geometry of bosonic subspaces is studied. It is shown, in particular, that the conventional superspace extensions of the coset manifolds AdS_2 x S^2, AdS_3 x S^3 and AdS_5 x S^5, which arise as solutions of corresponding D=4,6, 10 supergravities and have been extensively studied in connection with AdS/CFT correspondence, are not superconformally flat, though their bosonic submanifolds are conformally flat. We give a group-theoretical reasoning for this fact. We find that in the AdS_2 x S^2 and AdS_3 x S^3 cases there exist different supercosets based on the supergroup OSp(4^*|2) which are superconformally flat. We also argue that in D=2,3,4 and 5 there exist superconformally flat `pure' AdS_D supercosets. Two methods of checking the superconformal flatness are proposed. One of them consists in solving the Maurer-Cartan structure equations and the other is based on embedding the isometry supergroup of the AdS_m x S^n superspace into a superconformal group in (m+n)-dimensional Minkowski space. Finally, we discuss some applications of the above results to the description of supersymmetric dynamical systems.
Bandos Igor
Ivanov Evgeny
Lukierski Jerzy
Sorokin Dmitri
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