180 The Quantum Structure of Space and Tame
the person who should really answer this sits next to you [G. Veneziano].
analyticity.
S. Weinberg I see what you mean. So you include the point at infinity in the
N. Seiberg Yes.
S. Weinberg Oh well OK, thank you.
N. Seiberg The sign of my comment was not in this direction, it was actually in
the opposite. This usually signals locality and causality. But I am not aware,
maybe you can enlighten me on that, of an argument that this must mean
that there is underlying locality. There might be some weaker statement than
locality and causality which leads to the same kind of analyticity.
S. Weinberg Well, I have never been able to elevate it into a theorem; in my
courses, I taught quantum field theory in such a way that locality emerges out of
the requirements of Lorentz invariance plus the cluster decomposition principle,
and then the cluster decomposition principle is more fundamental than locality.
In fact, I think it would be an interesting challenge, to understand how cluster
decomposition emerges from something like string theory.
N. Seiberg That is a very interesting point, because in particular it means that
there could be something fuzzy and non-local at short distance, as long as when
you separate things, things are well-behaved.
S. Weinberg That is the real test. The locality, we can live without, but I do not
see how science is possible without the cluster decomposition principle.
M. Douglas As a candidate to a model with emergent time, how about 2D quan-
tum gravity coupled to c greater than twenty-five matter, where the Liouville
becomes time-like.
J. Harvey How about it?...
W. Fischler What is the requirement of analyticity, if the emergent space-time
N. Seiberg Well, if you have this asymptotic region, you can scatter particles...
W. Fischler No, I am saying, what if, there is no asymptopia that allows for an
S matrix. Or do we say that maybe the requirement of analyticity forbids such
space-times to be solutions of quantum gravity?
N. Seiberg I do not see anything wrong with compact space. It is very confusing,
but I do not see anything wrong with that.
W. Fischler Let me just give you an example: de Sitter space-time, there is no
S matrix. Asymptopia does not allow you to define such an object. So what
requirement do we have about analyticity in this case? Or do we say de Sitter
space-time is not a viable quantum mechanical solution to whatever theory of
quantum gravity?
N. Seiberg I am not an expert on the subject. Some people believe that this class
of questions and confusions perharps are trying to tell us that de Sitter space
is not a stable solution. Other people, including some people in this room,
strongly disagree with that.
and its asymptopia do not allow for an S matrix?
