  As in the preceding paper we aim at identifying the effective theory that
describes the fluctuations of the local overlap with an equilibrium reference
configuration close to a putative thermodynamic glass transition. We focus here
on the case of finite-dimensional glass-forming systems, in particular
supercooled liquids. The main difficulty for going beyond the mean-field
treatment comes from the presence of diverging point-to-set spatial
correlations. We introduce a variational low-temperature approximation scheme
that allows us to account, at least in part, for the effect of these
correlations. The outcome is an effective theory for the overlap fluctuations
in terms of a random-field + random-bond Ising model with additional, power-law
decaying, pair and multi-body interactions generated by the point-to-set
correlations. This theory is much more tractable than the original problem. We
check the robustness of the approximation scheme by applying it to a fully
connected model already studied in the companion paper. We discuss the physical
implications of this mapping for glass-forming liquids and the possibility it
offers to determine the presence or not of a finite-temperature thermodynamic
glass transition.
