  De Boer et. al. have found an asymptotic equivalence between the
Hamilton-Jacobi equations for supergravity in (d+1)-dimensional asymptotic
anti-de Sitter space, and the Callan-Symanzik equations for the dual
d-dimensional perturbed conformal field theory. We discuss this correspondence
in Lorentzian signature. We construct a gravitational dual of the generating
function of correlation functions between initial and final states, in
accordance with the construction of Marolf, and find a class of states for
which the result has a classical supergravity limit. We show how the data
specifying the full set of solutions to the second-order supergravity equations
of motion are described in the field theory, despite the first-order nature of
the renormalization group equations for the running couplings: one must specify
both the couplings and the states, and the latter affects the solutions to the
Callan-Symanzik equations.
