210 The Quantum Structure of Space and Time
doesn’t include gravity, which is well-defined. I find the discussion of compact
universes extremely puzzling. Nati said that he has no problem thinking about
closed universes, but how do you think about it, Nati, or how does anyone think
about what are physical observables in such situations?N. Seiberg Maybe I should clarify what I have in mind. I have a lot of problems
thinking about it, but I don’t see any obstacle to their existence.D. Gross Agreed, but given that they might exist, how do you think about them?
N. Seiberg Well, we have one example of this in two dimensions, which is the
quantization of the world-sheet of the string. This is a very concrete example.
J. Maldacena Yes, it seems that in order to have a description of these closed
universes, you have to allow yourself the possibility of not having an exact
description, that the fundamental description will be fundamentally not precise,
I think.
E. Silverstein In fact this can be borne out by holographically dualizing closed
universes in the same way that we do for Randall-Sundrum, where indeed the
dual description also has lower-dimensional gravity, and you can continue thatdown to two dimensional gravity plus a large amount of matter and obtain at
least a simplification of the problem, but one which illustrates the limitations
that you all are talking about.
A. Ashtekar David, what is wrong with gauge-fixing? So if you had closed uni-
verses, right, there is gauge-fixed description, and then of course there has to
be consistency checks that different choices of gauges will give you the same...
D. Gross As Nati emphasized, gauge symmetries are redundancies in our descrip-
tion of nature, and presumably there are, as the AdS/CFT duality beautifully
illustrates, formulations of generally covariant theories where there is no gen-
eral covariance needed since there are only physical degrees of freedom used todescribe the system, so...
A. Ashtekar Maybe I am saying the same.
D. Gross AdS/CFT is the one description of quantum gravity that is best defined
in our toolbox, and using the gauge theory description of quantum gravity in
10 dimensions there is no such thing a gauge fixing, because there is no gauge
to fix.B. Greene So just back to the general question of emerging space-time, I wonder,
and I am not sure about this, I wonder if it is worth trying to sharpen what
one means by emerging space-time, and perhaps Gary’s question highlights one
instance. You can imagine a situation as you were describing, Chern-Simons
theory with a zero metric, where you do have some background coordinate grid
and then you can imagine the metric emerging as opposed to the coordinate
system emerging, so one can ask: do we talk about emerging topology, emerging
differential structure, do we talk about emerging complex structure, and then
do we talk about emerging geometrical structure on top of those structures? I
mean, I have always wondered: do exotic differential structures have any real