Emergent Spacetime 205
diction in terms, that we do want theories to be based on simple equations,
therefore reduction, in that sense, seems to be absolutely necessary to me, and
if you do not have that, should you then not do something else, go into music
instead of theoretical physics? That is the question.
J. Polchinski So I would like to respond to Abhay’s comments from earlier and ask
a question. In canonical general relativity, you write the wave function in terms
of geometries at one time, solve the hamiltonian constraint, and time emerges
as correlations in that wave functions. But when you talk about emergent
gauge symmetry and AdS/CFT, there is something more that happens. Because
there’s a set of variables which are actually completely neutral under the gauge
symmetry, you don’t have a hamiltonian constraint, you have variables that
satisfy it trivially, and they’re related in a complicated way to the other ones.
But you can solve the theory, and write the observables entirely in terms of the
gauge invariant observables, the ones on which the hamiltonian constraint is
already solved. And the question then is: is there some analogue of this which
is known, say, in other approaches to quantum gravity?
J. Harvey Does anyone want to answer that question or respond to it? Nati?
N. Seiberg I think the answer is exactly the comment I made to Steve, that in
the matrix model description of two dimensional gravity this is exactly what
happens.
E. Rabinovici In regard to emerging space-times I have a comment. I think we
should attempt to use methods which we learned from statistical mechanics,
appropriately modified for gravity, to study possible phases of gravity. And
one phase which I think is necessary, we should study more, is that in which
a‘ is infinity, or in other words where the string scale vanishes. And I think
once we understand that, it could help also understand more the emergence of
space-time.
G. Dvali I just wanted to comment that all these important questions about
emerging nature of gravity and space-time at short distances, in the UV, prob-
ably should be also asked about large distances, in the infrared, because after
all, we only understand, experimentally at least, we only understand the nature
of space-time and gravity at intermediate distances, and we have no idea what
is happening beyond the centimeters, and we know that something is go-
ing on there, the universe is accelerating. Normally we are attributing it to a
cosmological constant, but it may very well be that string theory encodes new
far infrared scale, and so the nature of space-time and gravity gets dramati-
cally modified there. So space-time may emerge in the UV, and also it happens
something in the IR. This question also should be studied.
J. Harvey I think that is sort of along the lines of what Nati called the old ap-
proach to the cosmological constant problem, that there’s some confusion be-
tween UV and IR, which I think is perhaps old, but not completely forgotten.
J. Maldacena Yes, I was going just to mention that this question of very long
