Does an antiDeSitter space compensate the vacuum energy? Sometimes I read here or there that a problem with the electroweak vacuum is that it implies a huge positive cosmological constant. On other side, I also read that AdS spaces are not useful anymore for real world observations because we need to get a small positive cosmological constant at the end of the day.
I wonder, is it not possible to compensate one problem against the other? This is, having in the Lagrangian an anti-deSitter space with negative radius or order 246 GeV, and then breaking of the electroweak vacuum so that the final result is slightly positive. 
 A: In KKLT, a stable AdS vacuum is uplifted to a metastable dS vacuum by the addition of antibranes. And one way to get a Higgs mechanism in string theory is to have a single stack of branes separated into two, parallel, very close stacks. 
So let's suppose we have a KKLT-like construction in which there are two such adjacent stacks of antibranes. Since the existence of a Higgs VEV makes a modest contribution to the c.c. in field theory, it seems likely that in the string scenario, there will also be a modest contribution to the vacuum energy coming specifically from the existence of the gap between the two antibrane stacks, and not just from the existence of the antibranes per se - though I couldn't tell you the details, I'm just reasoning by analogy with field theory. 
However... again reasoning from the field-theoretic precedent... the contribution to the vacuum energy from the stringy Higgs VEV ought to be very small compared to other contributions whose weigh-off is the usual basis of the KKLT construction. So it may be unlikely for the stringy Higgs VEV, specifically, to be a "special" part of the total c.c. 
That is, we are saying that the observed c.c. is "X", the contribution from the stringy Higgs VEV is "H", and so the sum of all the other contributions to the c.c. must have been "X-H". And it seems this final quantity must be tuned very precisely, for the "H" contribution to be what pushes it over the line, because "H" is going to be much smaller than a lot of what has gone into "X-H". 
It's logically possible that there could be some reason, e.g. some mysterious symmetry, whereby the tiny "H" contribution is what specifically tips the balance into positive vacuum energy. But that would require new ideas and new evidence. 
