  An intense study of the relationship between certain quantum theories of
gravity realized on curved backgrounds and suitable gauge theories, has been
originated by a remarkable conjecture put forward by Maldacena almost one year
ago. Among the possible curved vacua of superstring or M-theory, spaces having
the form of an Anti-de Sitter space-time times a compact Einstein manifold,
have been playing a special role in this correspondence, since the quantum
theory realized on them, in the original formulation of the conjecture, was
identified with the effective superconformal theory on the world volume of
parallel p-branes set on the boundary of such a space (holography). An
important step in order to verify such a conjecture and eventually generalize
it, consists in a precise definition of the objects entering both sides of the
holographic correspondence. In the most general case indeed it turns out that
important features of the field theory on the boundary of the curved
background, identified with the quantum theory of gravity in the bulk, are
encoded in the dynamics of the coinciding parallel p-branes set on the boundary
of the same space. The study of p-brane dynamics in curved space-times which
are vacua of superstring of M-theory, turns out therefore to be a relevant
issue in order to verify the existence of the holographic correspondence. In
the present paper, besides providing a hopefully elementary introduction to
Maldacena's duality,
  I shall deal in a tentatively self contained way with a particular aspect of
the problem of p-brane dynamics in Anti-de Sitter space-time, discussing some
recent results.
