# What is gravity according to string theory?

1. Sep 12, 2009

### ensabah6

Is gravity a particle field on spacetime or is it the geometry encoded in spacetime itself?

Since strings is 10-11 D, does a mass-energy object curve all 10 dimensions of spacetime or only 4 dimensions?

Is there a problem of time in string theory as there is in canonical quantum gravity? What is the relation between the timelessness of the Wheeler-deWitt equation as a theory of quantum gravity and string theory quantum gravity?

When string theorist speak of the unification of the 4 forces, unifying gravity with the electro-strong, does that include unifying spacetime?

2. Sep 12, 2009

### atyy

It could be either, depending on what approximation you make. Gravity is not fundamental in string theory, and only emerges in some approximate regime.

In AdS/CFT or BFSS proposals, space is emergent.

Nathan Seiberg has an interesting chapter about emergent spacetime in
http://books.google.com/books?id=ZNr0jue-b9cC&dq=solvay+conference&source=gbs_navlinks_s

3. Sep 12, 2009

### javierR

In perturbative string theory, strings (not a particle field) sit on a spacetime background, which we can take to be flat for simplicity here. Then there are particular string modes
that are quantum spin-2 objects that we call the graviton. From a distance, these would look like point-particle gravitons. This point of view is therefore a lot like the field theoretic picture of gravitation in which the dynamical role is played by gravitons, and the picture of curved spacetime geometry is supposed to arise from coherent states of many gravitons. In string theory, the relation between the strings and curved spacetime arises because a theory with spin-2 strings moving on a fixed background requires the background spacetime to satisfy Einstein's equations of general relativity. However, note that, as in field-theoretic gravitation, we're talking about fluctuations on a background spacetime (which here we took to be flat just for simplicity).
[Strings don't appear in 11D M-theory.] Well, in light of what I said above, if there are graviton modes in the 10D theory, they mediate the gravitational interaction among the other string modes and the background spacetime is supposed to satisfy Einstein's equations in 10D.

There isn't such a problem in standard string theory, essentially because spacetime (general relativity) is not a fundamental player in the theory, which is a criticism of some. There are approaches to background independent string theory; but these address the problem in a different way from quantum geometric programs, in which Einstein's equations and spacetime itself are directly quantized, in which case the question of how time evolution works when your states are "timeless" naturally appears.

There are different contexts in which the word "unification" is used. When standard string theory talks of unification, one could mean that there is a single object in the theory: a string (open or closed). Just from this assumption, you get various interactions including gravitational. In the context of the unification of forces, the interaction strengths (couplings) are meeting. But in string unifications, there is no analog of a single gauge group that is supposed to encode the 4 forces, and no notion of spacetime/force unification in the sense you might mean. There are theories in which spacetime emerges from a more fundamental theory (including some non-perturbative string formulations), and perhaps one can find one that "unifies spacetime and the other interactions" as you might be asking about, such as in a single geometric framework. People have been trying for decades.

4. Sep 12, 2009

### ensabah6

javierR

Hey thanks, one question I have though is that you got gravity in 10D, but how does this relate to gravity in 4D, and gravity w/4D + 6D compactified dimensions? Are the higher 6 dimensions also dynamical?

5. Sep 12, 2009

### javierR

When you have compact dimensions, the 10D gravitational fields are split into the usual 4D ones + 4D vector and scalar degrees of freedom (representing gravitational degrees of freedom in the 6 spatial dimensions). This is reflected in the fact that the 10D metric tensor $$g_{MN}$$ becomes the 4D tensor $$g_{\mu\nu}$$, the 4D vectors $$g_{\mu m}$$ and 4D scalars $$g_{mn}$$ where M=1,..,10; $$\mu=1,..,4$$ are the 4D spacetime directions; and m=5,...,10 are the compact directions. The 6D, "internal", part of the spacetime is completely spatial so in itself there are no dynamics. Nevertheless, taken as a whole spacetime (6+3)+1, where "+1" is time, there is still full 10D gravitational dynamics even though 6 of the dimensions are compact (like a 6-torus, e.g.).

6. Sep 12, 2009

### ensabah6

As with earlier attempts to unify via higher dimensions, if spacetime is dynamical, why would only 4 large dimesions be dynamical but the 6 compact ones remain frozen and no dynamics?

7. Sep 13, 2009

### Haelfix

The full 10d manifold is dynamical as explained already. From the worldsheet perspective, the extra dimensions (alla Kaluza Klein) appear as fields over a point. So for instance in GR, the extra 5th dimension component of the metric describing both the extra compact dimension or the electromagnetic degrees of freedom are described as proportional to a field called the 'Radion' or geometrically as a fiber bundle.

8. Sep 13, 2009

### tom.stoer

Can you give us some links to recent review papers?

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