Emergent Spacetime 209
their coordinates all coincide (zl = z2 = z3), three strings interact when every
point on one string also belongs to another string. Forcing all three strings to
overlap completely by imposing z1(0) = z2(0) = ZQ((T) would indeed lead to
incurable UV divergences. Instead, the condition for having a string interaction
is more like momentum conservation, but in coordinate space, i.e. ~1+~2+~3 =
0 (where string bits of opposite orientation are counted with a relative minus
sign). This is how string theory provides its compromise between locality and
non-locality.
G. Veneziano May I take advantage to... I am just wondering, in view also of what
Sasha Polyakov has emphasized, namely that the AdS/CFT correspondence is
between an on-shell theory in the bulk and an off-shell theory on the boundary,
whether we should really see this as a correspondence, or, you know, just as a
tool, OK? After all, suppose on the boundary we manage to have QCD, just
QCD, no weak interactions, just QCD, then on the boundary itself, we just may
be interested in the only observable, which is the S-matrix on the boundary.
And that S-matrix on the boundary would not be in itself sufficient to determine
what goes on in the bulk. In other words, it looks to me that this on- versus
off-shell duality may mean that actually the boundary field theory is a tool
to-the off-shell boundary field theory is just a tool rather than an equivalent
thing.
A. Polyakov Well, you know, before you turned on gravity, you have a choice, then
off-shell quantities are more or less well-defined. You don’t have to consider
necessarily the S-matrix. I think this - what we were taught in the days that
field theory was despised, that the only thing which makes sense is the S-matrix,
which is actually true in the theory of gravity, almost true. But in normal field
theory, it is not true, so I think it’s quite appropriate that since we make the
contact between theory of gravity and the theory without gravity, on the gravity
side we must have only on-shell amplitude, while on the theory without gravity
side we may have all possible correlation functions, not necessarily on-shell.
J. Harvey It has always seemed to me that AdS/CFT should, you know, be per-
haps a precise statement, but should allow for inexact statements. I mean, after
all if we had discovered that we live in anti-de Sitter space with a very small
cosmological constant rather than de Sitter space, and we went to the experi-
mentalists in Fermilab and told them that what they observe and measure is not
real, because it’s not defined at infinity, I think they would regard us as rather
useless. So it is clear that there has to be room for a description that is, you
know, an exceedingly good approximation to observables defined at surfaces at
infinity that are defined in a local way in the bulk. But how to actually do this
within the machinery we currently have seems to me rather problematic.
D. Gross This indeed is a very deep problem, because we can imagine compact
spaces in general relativity, and then we have no local gauge-invariant observ-
ables and no place for a holographic description in terms of something which
