Report for the academic year - Libraries - Institute for Advanced Study

THE SCHOOL OF NATURAL SCIENCES
commute with one of the space coordinates. In the first paper, field theories on such a
space were shown to be seriously acausal and inconsistent with conventional Hamilton-
ian evolution. To illustrate these effects, the scattering of wave packets in a field theory
with such space/time noncommutativity was studied, and effects which seem to precede
their causes were found. Also, the theory was shown to describe rigid rods, which grow
instead of Lorentz contract as they are boosted. These field theories are evidently incon-
sistent and violate causality and unitarity.
Since open string theory in a background electric field is expected to exhibit space/time
noncommutativity, this raises the question of whether it also leads to such acausal
behavior. It was shown that this is not the case. Stringy effects conspire to cancel the
acausal effects that are present for the noncommutative field theory leaving the theory
consistent.
In a second paper with L. Susskind and N. Toumbas, open strings in a constant back-
ground electric field were analyzed further. The main difference between this situation
and its magnetic counterpart is that here there is a critical electric field beyond which the
theory does not make sense. This critical field prevents a limit in which the theory
becomes a field theory on a noncommutative spacetime from existing. However, an
appropriate limit toward the critical field leads to a novel noncritical string theory on a
noncommutative spacetime. Contrary to standard lore, these noncommutative open
string theories involve only open strings and no closed strings.
Extensions of these ideas were studied with R. Gopakumar, S. Minwalla and A. Strominger.
Here, limits of string theory were found leading to theories without gravity exhibiting new
surprising properties. These theories exist in six and fewer spacetime dimensions and their
underlying geometric structure is not yet clear. Unlike the noncommutative theories
which depend on a deformation of spacetime involving a two-index tensor, here the defor-
mation involves a tensor with three or more indices. The strong coupling limit of these
theories in the various dimensions was studied, and an interesting web of dualities was
found to relate them. This web includes all previously studied theories: commutative and
noncommutative field theories, the newly discovered noncommutative open string theo-
ries, the enigmatic little string theories and many others.
This was a year of consolidation in PROFESSOR FRANK WILCZEK'S work on under-
standing matter at high density, using QCD and asymptotic freedom. The major quali-
tative results that emerge in the lowest order of approximation, including confinement
and chiral symmetry breaking, are now pretty well understood. This approximation
becomes accurate as the density goes to infinity, but to treat problems of great physical
interest, and to make experimentally testable quantitative predictions, we need to do
better. Wilczek has some ideas for this, but they need more work.
Wilczek did extensive work with Jonathan Feng (IAS) and Konstantin Matchev
(Fermilab) on the physical consequences of low-energy supersymmetry. Specifically, they
pursued the "focus point" hypothesis for supersymmetry breaking. This is a new theoret-
ical idea which avoids some of the apparent difficulties in reconciling low-energy supersymmetry
with established facts. The group's main original contribution was to show
that the focus point hypothesis naturally leads one to predict the production of cosmo-
logically stable particles with density just sufficient to provide the astronomers' "missing
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