In article <IDpswM.M7v@campus-news-reading.utoronto.ca>,
George Jones <george_llew_jones@yahoo.com> wrote:

Here's my very longwinded attempt at an explanation. I don't know this
stuff, and what follows is my attempt to get some of the concepts
straight.

String theory, which string theorists trumpet as a potential theory of
everything, seems only to give mathematically sensible answers in
universes that have 9 or 10 spatial dimensions.

I've read 11. But more than we see now, anyway.

If our universe is
really like what the string theorists want, why don't we notice the
extra dimensions? String theorists' answer: because the extra spatial
dimensions are compactified - curled up on a scale so small that they
have yet to be noticed.

I've wondered if the compactification follows naturally from basic
assumptions, or if it's imposed to explain why we don't see the extra
dimensions.

In article <IDpswM.M7v@campus-news-reading.utoronto.ca>,
George Jones <george_llew_jones@yahoo.com> wrote:

"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:d1mn6m$f50$2@rainier.uits.indiana.edu...

In article <Pine.LNX.4.44.0503201944390.27399-100000@dill.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:

On Mon, 21 Mar 2005, Gregory L. Hansen wrote:

In article <Pine.LNX.4.44.0503201825500.27399-100000@dill.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:

The actual result had nothing to do with black holes being created.
What
they were talking about were objects in QCD, solitons actually, that
are
*DUAL* to black holes in a corresponding supergravity theory via the
AdS/CFT correspondence. There's no black holes. The interesting idea
is
that if this correspondence can be made more convincing, then this
could
be some of the first hard evidence in favor of string theory. I
haven't
poured over the result, and unfortunately I wasn't able to attend the
talk
he gave here last week.

What does it mean to be dual to a black hole?

Okay, I should say abit about what AdS/CFT correspondence is. I just read
about this not that long ago.
The idea is that you can connect a super-gravity theory on an
anti-deSitter space with a conformal field theory on the boundary of the
space. QCD can be treated like a conformal field theory in the limit of
massless quarks and no running of the coupling constant. Doesn't sound
much like QCD, but as a calculational tool it might be okay. Some pretty
hardcore theorists seem to think so at least. So essentially the claim is
that the fireball observed in RHIC corresponds to a non-perturbative
object in QCD, that in this limit of QCD as a CFT corresponds to a black
hole in the dual gravity theory on anti-deSitter space.
Does that make any more sense?

Well, there's more words, anyway. I'm not even quite certain whether
you're talking about gravity or an analogy to gravity. I thought there
was an energy scale associated with gravitational effects that was
unattainable for the forseeable future.

Here's my very longwinded attempt at an explanation. I don't know this
stuff, and what follows is my attempt to get some of the concepts
straight.

String theory, which string theorists trumpet as a potential theory of
everything, seems only to give mathematically sensible answers in
universes that have 9 or 10 spatial dimensions.

I've read 11. But more than we see now, anyway.

If our universe is
really like what the string theorists want, why don't we notice the
extra dimensions? String theorists' answer: because the extra spatial
dimensions are compactified - curled up on a scale so small that they
have yet to be noticed.

I've wondered if the compactification follows naturally from basic
assumptions, or if it's imposed to explain why we don't see the extra
dimensions.

In turns out that there is a mathematical equivalence (duality) between

Is that a duality with a technical definition like a form being the dual
to a vector, the dual being required for the dot product A_i A^i?

these 2 different physical situations: closed superstring theory living
in the 10-dimensional background spacetime AdS x S^5; conformal
supersymmetric Yang_Mills field theory living in the 4-dimensional
background of Minkowski spacetime. Under this duality there is a
mathematical correspondence between:

1) symmetry transformations on the 5-dimensional spacetime AdS and
conformal transformations on Minkowski spacetime;

2) symmetry transformations on the space S^5 and internal symmetries
of the Yang-Mills fields.

Because of this duality, it is possible to map (mathematically) a
physical situation in one scenario into a dual physical situation in the
other scenario.

As Creighton Hogg has said, after certain gross approximations QCD looks
like a conformal Yang-Mills field theory, so, in this limit, all of the
above applies. Horatiu Nastase claims that a fireball observed at RHIC
was produced by QCD effects that are dual to black hole effects in
AdS x S^5.

I'm not really familiar with black hole effects in AdS x S^5.

From what I've written so far, it seems that the correspondence is
purely mathematical, but there is a further identification (also
mentioned by Creighton) that may make it a little more physical. The
Minkowski space background for the conformal field theory can be
identified with a a boundary of the AdS x S^5 background spacetime of
string theory. The physics on the boundary is then considered to be
the "hologram" of the physic taking place in the full higher dimensional
spacetime.

Does this mean that the fireball is the result of a "real" black hole?
Apparently not - Nastase talks about the "our" 3+1 dimensional
spacetime and the "abstract" 10-dimensional spacetime.

As I said above, I know almost nothing (I hope to learn more) about this
stuff, so large parts of what I've written may be wrong.

Maybe an actual test of string theories can come out of this.