208 The Quantum Structure of Space and Time
but it seems difficult to have locality in both and so which is one supposed tochoose, or what principle determines that. I... Do you feel like that’s.. .that
there is a clear understanding of that, because I find that also very confusing?D. Gross It is clear, because of this ambiguity, that locality or even what we
mean by space-time is something like gauge invariance. It is a description that
is inherently ambiguous and there are different descriptions which are useful for
different purposes.
J. Harvey Right, but perhaps we are missing the additional gauge degrees of free-
dom that allow us to project in a clear way onto the different local descriptions
right now. You could imagine that there’s a formulation where1 guess people
have attempted this-where both the variable and the T-dual are there at the
same time but there is some additional redundancy.
M. Gell-Mann When I left this field and stopped following what was going on in
detail, people had proposed a version of string theory in which there’s another
variable running along the string, and when you have that, then you can say
that in a string vertex, the old string and the two new ones, or the two old
ones and the one new one, are laid along one another, so that there is exact
locality for every point on the string. It’s not a question of the center of mass
at all. And I assume that in the intervening years that hasn’t disappeared. It’s
a much more satisfactory way of treating locality.J. Harvey Alright. As a moderator I don’t feel obliged to answer any questions,
so if anybody else would like to answer that I’ll.. .the author of a textbook,
or...
G. Veneziano As far as I know, Murray is right, I mean, I thought that in -at least in some versions of string field theory ~ that is exactly what you do.
You put a local coupling in terms of strings, namely when three strings overlap
completely, then they interact. This is an invariant local concept, I think.D. Gross That is absolutely wrong. It is nice to be able to make absolute state-
ments. It is not true that strings interact when they overlap- were it the case
that string theory interaction consisted of a vertex where strings totally over-
lapped, it would be infinitely more nonrenormalizable than ordinary quantum
field theory, require an infinite number of constants, have no relation to two-
dimensional geometry, and be totally different than the string theory that we
know and love. Instead strings meet at one point (in light cone gauge) or overlap
on half their length (in the covariant open string field theory approach). The
problem is that, unless care is taken to define time carefully, this interaction
need not be local in time.
G. Veneziano That is what I thought was the Witten open string field theory
action, that it had really overlapping strings.
Note by the editors The discussion between Gross and Veneziano continued over
lunch during which the misunderstandings were elucidated. Summarizing: while