In a quantum field theory moduli are scalar fields without potentials and we define the quantum field theory for fixed asymptotic values of the moduli. Yet once we know all the observables for some fixed asymptotic values of the moduli, they contain complete information on the observables for any other asymptotic values of the moduli. The situation in a quantum theory of gravity is more complicated. We review these issues, describe the essential difference between quantum gravity in flat space-time and AdS space-time and the implications of these observations for possible holographic dual of string theory in flat space-time.