Emergent Spacetime 207given the ultraviolet-infrared connection we are not even sure of this. Since we
don’t know what that principle is then how do we know that, if space-time is
emergent, one time will emerge? One question about space-time that has not
come up here, which has always intrigued me, is why can we easily imagine
alternate topologies, alternate dimensions of space, different than what we see
around us, but it seems impossible to imagine more than one time. Is a single
time anthropically selected? (This is a modern strategy for eliminating things
you don’t understand.) Or is it simply impossible to imagine physics with more
than one time? So when you give up the foundational setting of physics, as
people are struggling to do, you really would like to know what principles lead
to a unique causal ordering.
The other comment I wanted to make was about locality in string theory and its
connection with causality or the analyticity of the S-matrix. This is something
we might understand. After all, we have the S-matrix in string theory, and we
can ask why is it analytic? Why is string theory causal even though strings are
non-local and do not interact locally, at least if you define space-time in terms
of the center of mass of the string (i.e. choose a gauge in which the center
of mass of the string is identified with space-time). In string field theory, for
example, the fields depend not on points in space-time, but on loops, and in
terms of the center of mass of the string, as Nati pointed out, the interations
of such fields are then non-local. But this is not the way to define space-time
in string field theory. In fact, locality becomes manifest and one can derive the
analytic properties of the S-matrix if you either work in light-cone gauge, where
strings interact at the same light cone time at a single point, or covariantly, ifyou define space-time to as the midpoint of the string, where the interaction
takes place (at least in open string field theory). In both of these cases one can
understand, in string perturbation theory, how locality and causality emerge
from the interaction of non-local objects such as strings. On the other hand we
do not know how to address what happens non-perturbatively. If we use the
AdS/CFT duality to non-perturbatively define ten dimensional string theory
we are hard pressed to recover locality in the bulk. In addition, in cases we now
begin to understand, we see non-local structures emerge from string theory,such as non-commutative field theories, as a description of dual theory on the
boundary. There is a whole program, which I would urge people to follow, to
explore, in the context of field theory, what kinds of non-localities are allowable
and controllable and sensible, expanding what we already know about the non-
local field theories that are healthy boundary theories dual to string theories in
the bulk.
J. Harvey One of the topics that Nati raised which I must say confuses me as well,
is in situations where-string theory on a circle for example-where in different
limits you would use one description or its T-dual. It’s very tempting to think