82 The Quantum Structure of Space and Time
3.8 Discussion
J. Harvey There is a five-dimensional supergravity formally similar to eleven-
dimensional supergravity, with a one-form potential with Chern-Simons term.Do you know whether there is a similar algebraic structure associated to that
supergravity in this particular limit?
T. Damour Yes, Kac-Moody algebras can generically be associated to supergrav-
ities, and even to ordinary gravitational theories in various dimensions.
A. Ashtekar If I consider the coset space dynamics as being fundamental, where
is fi?
T. Damour It is encoded in the eleven-dimensional Planck length.
A. Ashtekar It appears in the metric?
T. Damour: Yes, for instance R4 terms in the action are made dimensionless using
the Planck length.
F. Englert I am wondering whether your theory is not simply valid near a space-
like singularity for different reasons, namely that near a space-like singularity
you essentially only have the time-direction. After all, if you dimensionally re-duce gravity to one dimension you expect El0 as a symmetry. Near a singularity
this is verified because the problem becomes essentially one-dimensional.
T. Damour The singularity is used here as a tool to reveal a symmetry structure
which exists independently. Recall that here indeed one find El0 starting from
any dimension. One never sees E?, or other duality groups appear.Prepared comment by N. Turok.
E. Silverstein Wound strings might not get blue-shifted at the singularity, but
other modes will?N. Turok Other modes will be non-perturbative states like black holes, etc. If
perturbative gravity goes through the singularity, I would already be delighted.
Let us deal with the non-perturbative states later. If you work out are going to
be created at the crunch, the creation rate is proportional to 00 which can be
taken small.E. Silverstein They will not be created, but what if you send one in?
N. Turok If you send a black hole in ...
E. Silverstein Just send a perturbative mode in.
Answer by N. Turok An initial particle? A pragmatic answer is that the density
of particles going in will be negligeable. Still one should worry.A. Polyakov There is a comment I wanted to make, concerning singularities.
When we try to treat the Big Bang, Big Crunch singularities in string the-
ory, you write down a sigma-model and then try a one-loop approximation and
you find the Einstein equation with Friedman type solution. From the point of
view of the sigma-model, the singularity in such a solution is nothing but the