  The AdS Distance Conjecture proposes to assign a notion of distance between
AdS vacua in quantum gravity. We perform some initial developments of this
idea. We first propose more sharply how to define a metric on conformal
variations of AdS through the action. This metric is negative, making the
distance ill-defined, a property relating to the famous conformal factor
problem of quantum gravity. However, in string theory, variations of the AdS
conformal factor are accompanied by variations of the internal dimensions and
of the background flux. We propose an $\textit{action metric}$, which accounts
for all of these variations simultaneously. Accounting for the variations of
the overall volume of the internal dimensions can flip the sign of the action
metric making it positive. This positivity is related to the absence of scale
separation between the internal and external dimensions: the negative external
conformal contribution must be sub-dominant to the positive internal
contribution. We then focus specifically on the families of solutions of
eleven-dimensional supergravity on AdS$_4 \times S^7$ and AdS$_7 \times S^4$.
For these, there is only a single further additional contribution to the action
metric coming from variations of the Freund-Rubin flux. This contribution is
subtle to implement, and the unique prescription we find requires singling out
the radial direction of AdS as special. Adding the flux contribution yields an
overall total action metric which becomes positive for both the AdS$_4$ and
AdS$_7$ families of solutions. The final result is therefore a procedure which
yields a well-defined distance for these families of solutions.
