Thread: The Superstring "Landscape" View Single Post


Urs Schreiber wrote in message news:... > On Wed, 2 Jun 2004, Squark wrote: > > > What precisely is the configuration space that you are talking about? > > By the ADM method config space is the space of field configurations on > spatial hyperslices - Wheeler's "superspace" (not that of supersymmetry) or > some $min-$ or midi- superspace approximation thereof, retaining only a finite > number of degrees of freedom Now I see what you're talking about. Well, a Killing vector in this configuration space is essentially a continous global symmetry of the theory. However, Michael Douglas writes in "The statistics of M-theory vacua" (http://www.arxiv.org/abs/hep-th/0303194), page 12, that probably no such continous global symmetry exists. The article he is referring to (T.Banks and L.J.Dixon, Nuclear Physics, B307, 93) dates back to 1988 and is not avaible on the net, as far as I know, so unfortunatelly I have no access to it currently. I certainly know about no such symmetry. The one argument I can think about against it is that it would be associated with a conserved charged whose existence in a gravitational theory conflicts the no-hair theorem. > $\exp(E10)$ is shorthand for the "group" associated with the hyperbolic > Kac-Moody algabra E10. > > One reason to conjecture that this humongous group is the full configuration > space of M-theory is that apparently the full dynamics of 11D sugra is > obtained by geodesic motion in a (small) subsector of this group. I haven't peeked at the references you supplied yet, but it is far from obvious what would be meant by "the full configuration space pf M-theory". According to the definition you gave earlier, (classical) gravitational dynamics would not generate trajectories in this configuration space but rather subspaces of infinite dimension (and codimension), each such subspace corresponding to all of the spacelike slices of a given solution. I'd say the system is not described by a particle in configuration space but rather by and infinity-brane! Best regards, Squark.