Mathematical Structures^141dimensions?” What was the problem you were referring to?
A. Van Proeyen N = 1 in four dimensions. If you want to add a Fayet-Illiopoulos
term. As far as I can see, this is still necessary to uplift the potential to have it
in a de Sitter vacuum. You cannot add just a Fayet-Illiopoulos term in super-
gravity if you have a non trivial superpotential, unless the superpotential is not
invariant under the gauge symmetry that corresponds to the Fayet-Illiopoulos
term. It is something which is not well known but it is a restriction in N = 1
supergravity.A. Strominger And it is known to be impossible to do that or we just have not
figured out how to do it yet?A. Van Proeyen It is known to be impossible.
H. Ooguri It sounds like we need some response.
N. Seiberg Can you state very clearly what it is that is not possible?
A. Van Proeyen To add a Fayet-Illiopoulos term when you have a non trivial
S. Kachru Can I make a comment that is relevant?
H. Ooguri That will be the last comment.
S. Kachru Of course what happens in the supergravities is that the Fayet-
Illiopoulos terms become field dependent. Presumably in this model with the
anti-brane, what happens is that the Kahler mode upon which the D-3-brane
tension depends, which is included in the potential, has an axion partner. Thecoefficient of the superpotential that is used transforms by a shift under a gauge
symmetry. I think this makes the structure that was used in the original model
completely consistent with the field dependent F-I terms of supergravity. Do
you agree with that possibility?A. Van Proeyen Yes. I agree with the possibility. I have not seen a model, but
1 agree with the possibility.
J. Harvey The subject of the session is mathematical structures. I feel a certain
tension between Dijkgraaf’s beautiful talk about all the wonderful structures
that come out and the comment that Douglas made about how our hydrogen
atom is this maximally supersymmetric solutions. I have a feeling that, without
actual hydrogen atoms and helium atoms and molecules, a string theorists faced
with just the quantum mechanics of the hydrogen atom would discover you can
use S0(4,2) as a spectrum generating algebra. He would then generalise it to
SO(p, Q) rather than generalising to the helium atom. It is well recognised that
one of the central problems facing string theory is how to narrow our research
down to the investigation of the correct mathematical structures rather than
this infinite sea of beautiful possibilities. The connections are wonderful and
very inspiring. But how do we figure out which are the right directions to gowithout experiment, without data? This is not a new question, but I think
it would be very welcome to have some discussion at this meeting of how we
do this, how we try to connect string theory to data. Obviously these fluxsuperpotential.