  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.
