Re: interpretations of gravity graviton versus spacetime curvature

From: Kefka G (kefkag_at_aol.com)
Date: 09/16/04 

Date: Thu, 16 Sep 2004 12:09:21 +0000 (UTC)

Mark Palenik wrote:

>Isn't a large portion of string theory devoted to describing forces as
>
>curvature of space in a sort of kaluza-kline-esque way?
>

I'm not a string theory expert by any means, but from what I've gleaned, this
is not the way it describes forces. The flavor of a Kaluza-Klein approach is
as follows (forgive me, this is too simplistic to be totally accurate - there
are several nice expositions online):

1) Start with GR in n+1 spacetime dimensions
2) Curl up n-3 of these dimensions into some compact manifold
3) Look at the first Fourier mode of the field in the compact dimensions
(loosely: neglect all derivatives in any of those directions)
4) The isometry group of the compact manifold becomes the gauge group of the
3+1 Kaluza-Klein theory

But in string theory, the extra dimensions are compactified on Calabi-Yau
manifolds, which (if I remember correctly) admit no isometry groups, and hence
there really are no corresponding K-K theories since the main point of K-K
theory is (isometry-->gauge). Those manifolds are chosen so as to preserve the
consistency of the theory and effect a 3+1 interpretation, NOT to obtain the
forces in 3+1-D. In fact, (correct me if I'm wrong, please) I think that the
usual forces come out of the dynamics of the string in open dimensions, and the
K-K step is even more classical than it was originally intended - it's
analagous to the way that Maxwell's theory in 4+1-D looks a lot like the 3+1-D
theory if we compactify one dimension classically. (Even this step is somewhat
questionable, though - 4+1 compactified on a circle is not exactly the same as
3+1, for a whole host of reasons which I won't go into since this is a gravity
thread; for one, 4+1 Maxwell is not even renormalizable classically, so
something hinky is going on)

Or I could be wrong - I temporarily gave up learning string theory well before
I understood it all. It's quite possible that it's not that simple at all.
Maybe someone with a bit of expertise can clarify?

Mark:
>Although I don't really know anything at all about quantum field theory, my
>
>guess is that virtual gravitons, which would be responsible for transmitting
>
>the gravitational force, can be described as a series of perturbations to
>
>flat spacetime that, when summed up, look something like GR on a large
>
>scale.

This is essentially the "Feynman" approach (originally due to Deser, I think)
where Einstein's equations are derived from a massless spin-2 theory that is
made consistent by letting it act as its own source - the resulting theory is
(classically) identical to Einstein's as long as there's no topological funny
business (not surprising, as it is a perturbative theory and odd topologies
certainly can't be described as perturbations of flat space). Even the changes
in the propagation speed of light, time dilation, etc. come out of looking at
it this way. I think this, in fact, is exactly how GR comes out as the low
energy limit to string theory, since there is a massless spin-2 mode of the
string.

But it's worth repeating that one of the primary objections most gravity folk
have to string theory is that it is background dependent, i.e. it starts off
with flat spacetime of some given topology and lets gravity work like a regular
old force on that, rather than letting gravity alter the spacetime itself.
I've heard rumblings that string theory allows the background dependence to
"fade away" by allowing space-tearing transitions, etc., but I can't really
understand how that can happen when from the get-go it is formulated as a field
theory on the background...if the background spacetime is not a dynamical
variable of the theory, then how can it possibly change? I don't know, so I
must be misinterpreting part of the theory. Maybe in a non-perturbative
formulation (does one even exist?) the background is dynamical? Someone want
to help straighten this out?

-Eric

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