Random-field-like criticality in glass-forming liquids

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.