  We introduce an approach to derive an effective scalar field theory for the
glass transition; the fluctuating field is the overlap between equilibrium
configurations. We apply it to the case of constrained liquids for which the
introduction of a conjugate source to the overlap field was predicted to lead
to an equilibrium critical point. We show that the long-distance physics in the
vicinity of this critical point is in the same universality class as that of a
paradigmatic disordered model: the random-field Ising model. The quenched
disorder is provided here by a reference equilibrium liquid configuration. We
discuss to what extent this field-theoretical description and the mapping to
the random field Ising model hold in the whole supercooled liquid regime, in
particular near the glass transition.
