140 The Quantum Structure of Space and Time
4.4 Discussion
A. Van Proeyen I want to make a remark or maybe a question about the struc-
ture of KKLT (Kachru, Kallosh, Linde and Trivedi). As far as I know, there
is still no consistent supergravity framework for it. For the first step, there is
no problem when one uses the superpotential. But then the uplifting needs
D-terms which, as far as I heard, always needs the Fayet-Illiopoulos terms. But
that is not consistent if one has already put a superpotential. So I do not know
how this can be solved and brought into a consistent effective supergravity
framework. Or is there another mechanism that someone sees? As far as I can
see, the KKLT framework as a supergravity theory is just not yet consistent.
R. Kallosh In short, since 2003 when we attempted this uplifting, it was clear that
the supergravity has Fayet-Illiopoulos terms, but to get them from string theory
is rather difficult. So the best case we know today is when we have D7-branes
at the tip of the conifold and fluxes on it. From the perspective of string theory
this looks as close to a consistent D-term in supergravity as possible. At present
we cannot do better, but I hope that somebody will. It needs to be done.
H. Ooguri In that spirit I would also like to note that the study of the landscape
is still looking at a very limited range of the possible moduli space. There is
a big territory that needs to be understood. In particular, in the context of
developing mathematical tools to understand it, I would like to note that it is
very important to understand the stringy corrections to this program. I hope
to have some progress in that direction. I guess Kachru has a comment on that.
S. Kachru I completely agree with what you just said. This is more a comment
about the status of constructions. The initial construction used some kind of
configuration of branes to get a positive energy. But in fact if you look through
the literature that has been generated in the last three years, there are now
somehow an infinite number of proposals. The most mild one actually just
uses the F-term potential coming from fluxes themselves to give the positive
term. I actually do not see any possible inconsistency with embedding into
supergravity. Explicit examples that give examples where the F-terms are non
zero in the minima of the flux potential were actually constructed by Saltman
and Silverstein. The statistics of Denef and Douglas that were quoted by Lust
in giving lo5'' models, were actually more or less counting those vacua. So this
may be relevant to Van Proeyen's question.
A. Van Proeyen As far as I can see, as long as one only has the F-terms, one still
has vacua with a negative cosmological constant. You still need the uplifting.
S. Kachru No. My point was that the so-called uplifting can be done by non
vanishing F-terms because of the fact that the F-terms contribute positively in
the supergravity potential.
A. Strominger This sounded interesting but I did not catch the first statement:
"There is no supergravity known with an F-I-term and a F-term in how many
