  We study the transition of a scalar field in a fixed $AdS_{d+1}$ background
between an extremum and a minimum of a potential. We compute analytically the
solution to the perturbation equation for the vev deformation case by
generalizing the usual matching method to higher orders and find the propagator
of the boundary theory operator defined through the AdS-CFT correspondence. We
show that, contrary to what happens at the leading order of the matching
method, the next-to-leading order presents a simple pole at $q^2=0$ in
accordance with the Goldstone theorem applied to a spontaneously broken
dilatation invariance.
