Well it just so happens that Mitchell answered this question in a private email, I'm posting the relevant part here for the greater good.
The Wick rotation in this case transforms a local patch of dS space
into AdS space, or vice versa.
Think of the difference between concave and convex, a valley and a
hill. Then you should imagine that we have some formula appropriate
for a valley - e.g. you might have a line-of-sight device like
surveyors use, and you need to adjust the angle of the view finder, in
a way that depends on the curvature of the ground. We can turn it into
the corresponding formula for the hill by replacing, somewhere in the
formula, a positive number with a negative number - because the
curvature now has the opposite sign. This is what's actually going on
in these Wick rotations, although the details are somewhat more
Returning to the analogy, turning dS space as a whole into AdS space
is like turning the whole valley into a hill.
Here is a picture for the analogy. Scroll down to the concave meniscus
vs convex meniscus.
In the concave meniscus, the vectors normal to the surface (labeled R)
diverge; in the convex meniscus, they converge.
In the previous paragraph, you can see two formulas, basically "Force1
minus Force2" and "Force2 minus Force1", which correspond to the two
situations. You can get one formula by multiplying the other by -1.
So here is the analogy. If you start with the force formula for a
concave meniscus, and want to get the force formula for a convex
meniscus, you perform the transformation "multiply by minus 1". That's
analogous to: start with the quantum propagator for a scalar field in
AdS space, and get the propagator in dS space by the transformation
"perform a Wick rotation".
But if you actually want to turn a concave meniscus into a convex
meniscus, you're not just "multiplying the meniscus by minus 1". What
you would have to do is increase the intermolecular tension
everywhere, until it changes the curvature.
In the same way, the uplift from AdS space to dS space involves
changing the local curvature everywhere, by having extra fields whose
energy density acts as an extra source of curvature (this is in the
"Landscaping" paper by Silverstein and Polchinski).
So my first point is that uplifting isn't Wick rotation. It actually
means that you add something to your model, which will make the space
curve differently. What the Wick rotation allows you to do, is to take
a formula appropriate for one type of space, and modify it so it
applies to the other type of space - but these are formulas which
describe what happens in a small patch of the space, they aren't
describing its total structure.
So far, I've only been talking about physics in the bulk (dS or AdS).
The existence of a boundary CFT, and the details of how it relates to
the bulk physics, wasn't even discussed yet. Remember that half of
what David Lowe writes about is just a mapping from the center of the
bulk to the edge of the bulk, that is, it's something entirely within
bulk physics. For example, it's about how the wavefunction of a
particle changes as it travels from the interior to the edge. Then, at
the edge of the bulk, is the truly holographic mapping; or at least,
the edge of the bulk is the place where a point in the bulk maps to a
single point on the boundary. (Points deep in the interior of the bulk
correspond to some sort of sum over whole regions on the boundary.)
The truly holographic mapping is this change in variables - from bulk
variables to boundary variables.
So a big part of what we should be interested in is, what happens to
the holographic change in variables if we go from AdS to dS. But there
might be an easier case to study first: what happens to this change in
variables if the curvature of AdS space changes (this would usually be
expressed in terms of the "radius" of the AdS space, the distance from
center of bulk to edge of bulk).
If you look up the notes of Thomas Hartman's talk from Strings 2011,
he actually says how the boundary theory changes for Vasiliev's
higher-spin gravity, as you go from AdS to dS. In AdS space, the
boundary theory is a vector field theory with an O(N) symmetry, in dS
space the boundary theory is now a scalar field theory with a Sp(N)
symmetry (N is the number of vector fields or number of scalar
fields). So going from AdS to dS requires the set of fields to change
rather radically - though apparently there's still enough of a
similarity that he and Anninos were able to deduce or guess that Sp(N)
symmetry would be the dS counterpart. (Let me also say in passing that
they have only solved the problem - if they have solved the problem;
no paper yet... - for a particular case of AdS/CFT. When the bulk
theory is string theory rather than Vasiliev's higher-spin gravity,
the boundary theory is a supersymmetric field theory that Hartman
doesn't know how to transform appropriately; he says this in questions
after his talk.)
If you see Hartman's notes, I think you'll also find that he talks
about the cosmological constant in the bulk space going from negative
to positive. This just refers to the curvature, and the difference
between AdS and dS. But you can also talk about the difference between
AdS with strong curvature and AdS with weak curvature. This also
requires a change in the boundary theory, but not such a big change.
One reason AdS/CFT is popular is that it is a 'strong-weak' duality.
When quantum theories have strong "couplings" - when the interactions
are strong - they become difficult or impossible to calculate with,
because the usual approach of successive approximations - perturbation
theory - doesn't work. The whole idea of perturbation theory is that
each correction is smaller and less important than the last, so in
order to approximate the actual result, you just keep adding smaller
and smaller corrections. But when the interaction is strong, the
corrections get bigger as you go, which means that the whole starting
point was wrong.
In AdS/CFT, typically, when the boundary theory is strongly coupled,
the bulk theory is weakly coupled, and vice versa. So if you have a
strongly coupled field theory, it may have an AdS dual gravity
description which is weak and therefore calculable. Or if you have a
gravity theory in a strong coupling state, it may be dual to a weakly
coupled boundary field theory.
If the curvature of the AdS space gets bigger, that should mean that
the gravitational coupling is getting stronger, but in turn that means
that the boundary coupling is getting weaker. And conversely, if the
AdS space is getting flatter - more weakly curved, and approaching the
transition to dS space - that should mean the boundary theory is
getting strongly coupled. And even independently of AdS/CFT, it's well
known that strongly coupled theories often have a dual description in
terms of new variables which will be more easy to calculate with. So
possibly this is an aspect of what happens on the boundary as you go
from AdS to dS.