String Theory and Spacetime - Some Questions

[inflector]

From what I've read, String Theory is a theory of everything, unlike some of the other quantum gravity theories. That means that String Theory explains other particles and fields including gravitons. So String Theory is a quantum gravity theory because it includes gravitons.

But I was wondering, what is spacetime in String Theory? Does it exist as a separate entity? Is there some special gravitational gauge field?

Or does the GR concept of spacetime not appear in String Theory?

How does the concept of time appear in String Theory? Is it like quantum mechanics or GR or something completely different?

 

[atyy]

In perturbative string theory, spacetime appears in two ways. First, as a background on which strings move. For string theory to be consistent, this background must be a solution of general relativity. Secondly, as a graviton, which is an excited state of a string. This would seem schizophrenic, except that a coherent state of gravitons (the second sense of spacetime) is a background spacetime (the first sense of spacetime). There is a discussion of this following Eq 7.1 of http://arxiv.org/abs/0908.0333: "Although it’s obvious that (7.1) describes strings moving in curved spacetime, there’s something a little fishy about just writing it down. The problem is that the quantization of the closed string already gave us a graviton."

In some forms of non-perturbative string theory, like AdS/CFT, some parts of a higher dimensional spacetime are "emergent" from non-spacetime quantities in a theory with a lower dimensional spacetime. Try section 5.3 of http://arxiv.org/abs/hep-th/0601234, or figure 1 of http://arxiv.org/abs/0909.0518.

An interesting reference which talks about spacetimes emerging from entangling two different quantum systems can be found in section 3 of http://arxiv.org/abs/0907.2939: "In this section, we will argue that quantum entanglement between the non-perturbative degrees of freedom corresponding to different parts of spacetime plays a critical role in connecting up the emergent spacetime."

 

[atyy]

http://blogs.uslhc.us/nima-arkani-hameds-messenger-lectuers

The lecture "spacetime is doomed" is interesting.

 

[haushofer]

I found the lectures of David Tong very useful. What one can do is to write down the Polyakov action in a general curved spacetime background. But ofcourse, just as a laserbeam is made out of photons, this spacetime should be made out of gravitons.

Now, on the worldsheet one has conformal symmetry (this is needed for instance in order to identify the original ansatz, the Nambu-Goto action, with the Polyakov action which is quantizable). Conformal symmetries have a map called the "state-operator map". This map tells you that the states of the CFT are in 1-1 correspondence with the local operators in the theory. This enables you to describe graviton states via local operators called vertex operators.

Now the funny thing is that one can show that the generalization of the Polyakov action to curved spacetime backgrounds can be seen as the extension of the flat spacetime action to the curved spacetime action via inserting these graviton vertex operators.

The nice thing about string theory is that it constraints spacetime, but ofcourse one first has to assume there exists something like that. If you do that, properties like the number of spacetime dimensions follow. From the CFT point of view for instance, in the bosonic case gauge fixing occurs via ghost fields (a trick to gauge fix and preserve Lorentz invariance also used in QFT). These ghost fields contribute -26 to the central charge. However, the Weyl anomaly (quantum effects which treathen to spoil conformal invariance on the world sheet) is proportional to the total central charge and should be zero. The solution is to add 26 scalar fields X with central charge 1 each: the 26 spacetime dimensions.

Another way to see this need for D=26 dimensions is via lightcone quantization; the Lorentz algebra has to be preserved after quantization, and one of the Lorentz commutators is asking you then to put D=26.

Hope this helps :)

 

[inflector]

Thanks atyy and haushofer. I'll read those references over.

 

[tom.stoer]

Inflector,

I think that there is one central issue with many approaches of quantum gravity, namely background independence. Starting with a split of spacetime into a classical (fixed) background and some fluctuations (gravitons) on top of if will fail in many cases. Ordinary gravity / GR cannot be quantized in that way; it fails to be perturbatively renormalizable, i.e. the theory will lose its predictive power. The situation seems to be better in string theory and possibly maximal 4d SUGRA which could be finite order by order in perturbation theory - which does not mean that the perturbation series itself does converge (there are reasons to assume that it diverges). So even in string theory and SUGRA this lack of background independence is a central issue.

I think it's rather trivial that splitting spacetime into a background plus fluctuations on top of this background plus quantization of the fluctuations prevents us from understanding the background in terms of these fluctuations. This does not only apply for quantum gravity but even for ordinary quantum field theories. So what one needs is a theory that allows one to quantize gravity w/o introducing this artificial split - and that goes beyond perturbation theory. I think this is accepted in all main approaches for quantum gravity.

But that automatically means that the concept of gravitons will change. They are no longer small fluctuations on some background but they are the full dynamical degrees of the gravitational field. There are some approaches working along these approaches: LQG, CDT (as a computational tool), AS (don't confuse the background method used in AS with fixing a background; here the idea is to keep the background generic) and some approaches within string theory (especially AdS/CFT).

Succeeding with this non-perturbative, background independent quantization will automatically explain what spacetime "is at the fundamental level.