# Why I am REALLY disappointed about string theory

marcus
Gold Member
Dearly Missed
In LQG there are NO gravitons at the fundamental level.
Current status of the LQG graviton propagator:
http://arxiv.org/abs/0905.4082
You know the story at least as well as I do. The graviton is a mathematical concept primarily at home in a stable flat geometric setting. High energy means curved unstable geometry. No question of gravitons being "fundamental", in the usual sense of a high energy regime. The graviton propagator for then-current LQG was derived around 2006, then a new spinfoam vertex got established around 2008 and the calculations are being repeated.
Corrections welcome if anyone has more up-to-date information about the LQG, or a better way to summarize the situation.

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Looks like they get something similar in a particular limit and a particular gauge. In any case, there are two options now:
1)they get the correct answer to all orders etc
2)they don't

1)they'll have to explain the KLT relations. oops, they can't because they don't have any gauge theory do they?
2)they'll say that gravitons aren't real anyway so who cares

Btw I also noticed some susy LQG papers? What's up with that? If susy can be incorporated into LQG, I'll be anxiously awaiting their interpretation of ads/cft.

So at this time I really don't think we should keep getting LQG in this discussion, when we're talking about consistency, predictions, or basically anything like that. We're getting too off-topic with LQG speculations.

MTd2
Gold Member
Then quantum mechanics is wrong.
This is like saying that a water flux must be quantized otherwise quantum mechanics must be wrong. Only very special cases of fluxes, like He4, have some sort of quantization. Water is quantized in H2O molecules, He3 at 1K has an effective quantization as a "quantum liquid", superfluid. Hmm, and I am not really talking about LQG here. Just saying what is happening with Erik Verlinde, so that you can already be aware when other people come to you and say these things.

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So at this time I really don't think we should keep getting LQG in this discussion, when we're talking about consistency, predictions, or basically anything like that. We're getting too off-topic with LQG speculations.
I fully agree; it's a nice detour, but does neither help to understand gravity in the context of string theory nor unification of other forces with gravity which is not the focus of LQG.

So again I would like to come back to the list of questions

• what string theory really is
• what the fundamental principles are and how the final theory will look like (in terms of strings or other fundamental degrees of freedom)
• what the major obstacles (inherent to string theory) are preventing us from identifying these underlying principles and constructing this unique framework or theory

and I would like to ask if one should add the nature of fully dynamical gravity and/or geometry as another deep question. I would say "no", perhaps as one example of an onstacle, but not as a fourth question.

Gravitons in string theory - fine; some sorts of black hole calculations - fine; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independet geometry. Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collaps of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.

Afaik one can get around this problem in AdS/CFT (I do not understand the details here) because one is able to translate gravity into CFT w/o gravity such that dynamical geometry is represented by dynamical fields on a background. In that sense the theory is fully background independent except for the AdS which is more a topological superselection sector (due to its boundary conditions), but within AdS geometry is allowed to fluctuate freely.

If this is true (that means if I understood correctly) the problem of background independence has been solved in the AdS/CFT context (on the CFT side), so all what remains to be done is to allow for other spacetimes like dS etc.

And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)

http://egregium.wordpress.com/2007/05/24/is-there-more-to-gravity-than-gravitons/" [Broken]

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MTd2
Gold Member
Let me quote the above paper:

http://arxiv.org/abs/gr-qc/0409089

From Gravitons to Gravity: Myths and Reality

(Submitted on 23 Sep 2004)
There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full non-linear Einstein's theory of gravity by coupling a massless, spin-2 field $h_{ab}$ self-consistently to the total energy momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein-Hilbert action and (iii) it only uses standard concepts in Lorentz invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect -- and critically re-examining several previous attempts -- we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is \textit{impossible} to obtain the Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly. Second, we use the Taylor series expansion of the action for Einstein's theory, to identify the tensor $\mathcal{S}^{ab}$, to which the graviton field $h_{ab}$ couples to the lowest order. We show that the second rank tensor $\mathcal{S}^{ab}$ is {\it not} the conventional energy momentum tensor $T^{ab}$ of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein's theory with the source being spin-0 field, spin-1 field or relativistic particles by explicitly coupling the spin-2 field to this second rank tensor $\mathcal{S}^{ab}$ order by order and summing up the infinite series. Finally, we construct the theory obtained by self consistently coupling $h_{ab}$ to the conventional energy momentum tensor $T^{ab}$ order by order and show that this does {\it not} lead to Einstein's theory. (condensed).

*************

Padmanabhan is the guy who Verlinde bases his holography, without gravity, ideas.

atyy
I have pretty much all the same questions as a layman as tom.stoer's long post #129 (except I think of it as "what's exciting in string theory?").

But regarding the question of background independence in perturbative string theory, is it really that a propagating string cannot change the background geometry? After all, the string contains the graviton, and the graviton is geometry. Like in perturbative classical GR, where the full metric g=background+h. The theory is still at least somewhat background independent, since actually only g will turn out to be observable, and it will get its dynamics from h. The problem with perturbative classical GR seems to be that it is perturbative, I think, more than that it is background dependent (but am not sure about this, since the attempt to get a non-perturbative equation for background+h with dynamics restricted to h can get you to almost the full equations, but not quite, since it requires that spacetime can be covered by harmonic coordinates, Eq 62 and following discussion in http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken])

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So again I would like to come back to the list of questions

• what string theory really is
• what the fundamental principles are and how the final theory will look like (in terms of strings or other fundamental degrees of freedom)
Obviously no one can answer these for sure, this is an unfinished theory, and all what one can do is inspired speculations. I had outlined mine above.

• what the major obstacles (inherent to string theory) are preventing us from identifying these underlying principles and constructing this unique framework or theory
I think the following is not inherent to string theory except the last one:

Computational difficulty… lack of human intelligence....armchair experts who try undermine the effort

It is simply not so that one is able to compute anything, even for a completely well-defined theory (try to analytically compute the hadron spectrum from the QCD langrangian, eg. And anything having to do with gravity is going to be much more complicated). So that's why supersymmetric toy models are so useful - as many things can be computed, sometimes even exactly. This is a quite non-trivial feat and source of a lot of excitement, as well as of many conceptual insights. Whether one would ever be able to get beyond studying toy models.. I don't know, but I doubt it.

; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independet geometry.
I don't think that anyone claims this!

Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collaps of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.
This is very true; at least for the on-shell formulation of string that we know. There is simply no known formulation which would allow to "compare" different backgrounds, describe tunnelings, etc, as all this would require an off-shell formulation that we don't have. Some limited toy models exist here and there, eg some insights can be gained by considering tachyon condensation, which is a model for relaxing to a ground state. Some other toy models for going off-shell are topological strings where one can identify on-shell vacua as critical points of off-shell superpotentials. AdS/CFT provides a background-independent setup in a certain sense, for a specific situation, but this also doesn't allow to address questions of vacuum selection or Calabi-Yau's, etc.

Obviously one of the major missing points in string theory is the lack of an off-shell, perhaps background independent formulation; I guess no one would contest this statement… it's hardly a point of disagreement for string physicists!

And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)
In would say if gravitons turn out not to exist, string theory is dead (in the sense of unification with gravity); it still would be relevant for gauge theories, and describe QCD strings etc.

Haelfix
The geometry definitely can change (and in fact the topology can too) in a dynamic way, then there are backreactions and consistency checks that can be performed to ensure that you were in fact correct. Of course if the geometry change is too violent, the higher orders of perturbation series do become important and then for lack of a calculational scheme to compute them, you either have to guess the answer, invent a new nonperturbative method or look for some sort of duality.

However the only problem that I am aware off is that explicit examples of calculations are horribly messy and unlovely and its hard to do in full generality, but then that shouldn't be so surprising. ADM calculations are often messy as well.

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MTd2
Gold Member
Would a non perturbative formulation of string theory help with an off shell formulation?

BTW, I think it is strange to talk about even about the existence of a background for a string theory, right?. Anything in string theory is about string interactions, even dimensions are fields on the worldsheet.

MTd2
Gold Member
The thing I don't like in string theory is really, really, very simple. LQG, Asymptotic Safety, GR, Quantum Mechanics, String Theory are very beautiful theories, all of them with a degree of non-intuitiveness. This part of not being non intuitive, and making us change our perception is really cool, but what bother's me is how spin is taken for granted whereas all other quantum numbers can be obtained from something else.

I mean, It really bothers me is that there is no justification for the origin of spin.

marcus
Gold Member
Dearly Missed
I have to say this exchange impresses me by its modesty forthrightness and absence of obfuscation. "Surprised" gives a professional perspective on his own branch of research which allows room for other approaches. Congratulations to both parties here:

It is simply not so that one is able to compute anything, even for a completely well-defined theory (try to analytically compute the hadron spectrum from the QCD langrangian, eg. And anything having to do with gravity is going to be much more complicated). So that's why supersymmetric toy models are so useful - as many things can be computed, sometimes even exactly. This is a quite non-trivial feat and source of a lot of excitement, as well as of many conceptual insights. Whether one would ever be able to get beyond studying toy models.. I don't know, but I doubt it.

Originally Posted by tom.stoer
; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independent geometry.​

I don't think that anyone claims this!

Originally Posted by tom.stoer
Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collapse of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.

This is very true; at least for the on-shell formulation of string that we know. There is simply no known formulation which would allow to "compare" different backgrounds, describe tunnelings, etc, as all this would require an off-shell formulation that we don't have. Some limited toy models exist here and there, eg some insights can be gained by considering tachyon condensation, which is a model for relaxing to a ground state. Some other toy models for going off-shell are topological strings where one can identify on-shell vacua as critical points of off-shell superpotentials. AdS/CFT provides a background-independent setup in a certain sense, for a specific situation, but this also doesn't allow to address questions of vacuum selection or Calabi-Yau's, etc.

Obviously one of the major missing points in string theory is the lack of an off-shell, perhaps background independent formulation; I guess no one would contest this statement… it's hardly a point of disagreement for string physicists!

Originally Posted by tom.stoer
And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)​

I would say if gravitons turn out not to exist, string theory is dead (in the sense of unification with gravity); it still would be relevant for gauge theories, and describe QCD strings etc.

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I mean, It really bothers me is that there is no justification for the origin of spin.
How about the unitary (projective) representations of the Poincare group? For particles with mass $$m^2>0$$, the little group is $$SU(2)$$ aka. spin. Thus spin is a consequence of relativistic symmetries.
Maybe you have something more subtle in mind?

I mean, It really bothers me is that there is no justification for the origin of spin.
Even an un-quantized classical Dirac field has spin, i.e. the conserved Noether charge associated with rotations is a sum of orbital angular momentum and intrinsic angular momentum. A classical Dirac field is nothing but a system of linear PDEs! If spin is a valid concept in something as elementary as a system of linear PDEs, why is there any mystery about it? What I'm trying to say is that although spin is discovered in the weird quatum world, the notion of (unquantized) intrinsic angular momentum is possible even classically. (Although a classical Driac field is irrelevant to physics.)

MTd2
Gold Member
Maybe you have something more subtle in mind?
More subtle in mind. Every quantum number on a low energy effective theory can be related to a specific compactification of branes to where string attach. So, you have an explanation from more fundamental objects. Except for the spin. Note here that we are talking about a surface, so I keep wondering why not looking for some kind of vorticity quantization because of topological considerations.

Sorry for interrupting this discussion.

Thanks a lot for your patience and you continuing interest - but I have to step out for a while. I will stay in the mountains (alps, Europe) for hiking and climbing. Hope I'l be back in a while and still find this thread active.

Tom

marcus
Gold Member
Dearly Missed
Hope I'll be back in a while and still find this thread active.
I don't know if one can expect steady continued activity. But even if it is quiet for a few days I still expect that the activity will start back up when you return. Have a a great time in the mountains!

Bad wheather, so I will stay for another day :-)

After all, the string contains the graviton, and the graviton is geometry. Like in perturbative classical GR, where the full metric g=background+h. The theory is still at least somewhat background independent, since actually only g will turn out to be observable, and it will get its dynamics from h.
I think it is strange to talk about even about the existence of a background for a string theory, right?. Anything in string theory is about string interactions, even dimensions are fields on the worldsheet.
Regaring background independence: the problem is rather simple and one can see it already it 26-dim. bosonic string. The fundamental variable is Xa(s,t), with a=0..25 and s,t are the worldsheet coordinates. The string action contains XaXa so one contracts a in 26-dim. using a metric. It's exactly this metric that is not dynamical.

The geometry definitely can change (and in fact the topology can too) in a dynamic way, then there are backreactions and consistency checks that can be performed to ensure that you were in fact correct.
What I know is that the CY topology can change. The "global topology" will not change due to "superselection rules" or something like that; I guess it's like a topological conservation law, something that forbids e.g. tunneling from a kink to an anti-kink in the Sine-Gordon model due to the potential barrier.

What I don't inderstand is how (e.g. in the classical world sheet formulation) you can either plug in or get out a dynamical target space metric.

What I see is that if you map gravity => CFT then via changing something in CFT dynamically you automatically change the geometry after the inverse mapping CFT => gravity.

Nevertheless in the original formulation you still have the problem that all strings ("gravitons") are not able to change the background geometry. That means (as you say) that it's horribly complicated to do or understand these calculations. But this is exactly the point: if you start with the FRW k=+1 metric in GR you will by no means be able to find FRW K=-1 or Kerr by perturbation series. So in order to get the big bicture I think one must address this weak point of the theory.

One question: I asked for string field theory, but it was said (by Witten) that this is too messy to be true; then you are talking about an off-shell formulation which is missing. But isn't this string field theory?

Haelfix
Well, going from K=1 FRW to K = -1 FRW I think is probably something you wouldn't want String theory to show, since it is classically forbidden (then again who knows what quantum mechanics can do). But I think the gist of your post is correct.

Its worth recalling a few terminology points for the readers. A background in string theory has considerably more information than a background in GR. That is to say, the metric is only one field amongst many.

Also its worth emphasizing what can be shown in principle, vs what can be shown explicitly.

The fact that you have gravitons and a target space that satisfies einsteins equations exists does tell you a few things. It tells you that in principle a coherent state of many of these gravitons can and will form a gravitational wave that will change the target space metric dynamically. However, just like in the case of QED, you don't see many people working out explicit details of how a coherent state of QED photons changes the classical EM field. Instead you simply work with Maxwell's equations when doing classical calculations directly for most practical purposes.

So I think the point is that we are less interested in how the classical metric changes in isolation, and more with how the generalized quantum background changes in string theory, and that is important. Unfortunately as Surprised explained, there you really do need an offshell formalism to work it out in generality as opposed to a few explicit examples (usually discovered with dualities) or a few toy models where you have to bend over backwards via many picture changing operations to finally arrive at a result.

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I don't want to go from k=+1 to k=-1. I only want to say that if you would use k*1 as background, that you can't construct k=-1 simply by using perturbation theory.

So a background dependend formalism with perturbation expansion hides certain aspects of the theory, namely (if you start with k=+1) that k=-1 exists and that there is a very easy connection, namely simplychanging K=+1 to k=-1. If you start with only one background and if you only nw this background, you have no chance to explore the whole space of solutions.

That's what happened in string theory. There is no global picture that allowes you to look at the whole theory. You can only look at individual pieces and hope to be able to constuct dualities or something like that.

I was thinking that string field theory would provide something like this global picture.

Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism

atyy
I was thinking that string field theory would provide something like this global picture.

Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism
I think these have been known for many years as major questions that many would like to have solved. Polchinski wrote very similarly to you, suprised and Haelfix http://blogs.discovermagazine.com/cosmicvariance/2007/05/21/guest-post-joe-polchinski-on-science-or-sociology "If you have the flat spacetime S-matrix, you actually know a lot about curved spacetime, since you can form a very complicated geometry by throwing together a lot of gravitons in a coherent state. From a particle physics perspective, where the goal is to measure the underlying Lagrangian, this is enough: the S-matrix encodes all local physics in curved spacetime. Further, with this effective Lagrangian one can study processes in a fully curved spacetime, as long as the curvature stays below the string scale. One can then list things that are not covered by this: first, cosmological questions like initial conditions and spacetime singularities, and these are indeed open questions and the subject of active research"

I too would like to know: what is the current thinking on string field theory? 5 years back, Taylor's review http://arxiv.org/abs/hep-th/0605202 speculated that "String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory."

Is development slow because it is difficult, or is now thought not to be the way forward any more (just like matrix models like BFSS or IKKT are no longer thought to be completely general non-perturbative formulations, compared to 10 years ago)?

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marcus
Gold Member
Dearly Missed
Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism
As a footnote, here's the first paragraph of a 1993 paper by Edward Witten:
==quote==
Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach. Moreover, some highly simpliﬁed special cases or analogs of the problem, which look like they might be studied for practice, have also resisted understanding.
==endquote==
http://arxiv.org/pdf/hep-th/9306122

marcus