Six-dimensional supergravity on S3 x AdS3 and 2d conformal field theory

In this paper we study the relation between six-dimensional supergravity compactified on S-3 X AdS(3) and certain two-dimensional conformal field theories. We compute the Kaluza-Klein spectrum of supergravity using representation theory; these methods are quite general and can also be applied to other compactifications involving anti-de Sitter spaces. A detailed comparison between the spectrum of the two-dimensional conformal field theory and supergravity is made, and we find complete agreement. This applies even at the level of certain non-chiral primaries, and we propose a resolution to the puzzle of the missing states recently raised by Vafa. As a further illustration of the method the Kaluza-Klein spectra of F-theory on M-6 X S-3 X AdS(3) and of M-theory on M-6 X S-2 X AdS(3) are computed, with M-6 some Calabi-Yau manifold. (C) 1999 Elsevier Science B.V. All rights reserved.