A critical look at strings - Carlo Rovelli

[tom.stoer]

http://arxiv.org/abs/1108.0868
A critical look at strings
Authors: Carlo Rovelli
(Submitted on 3 Aug 2011)
Abstract: This is an invited contribution to the Special Issue of "Foundations of Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations". I have been asked to assess string theory as an outsider, and to compare it with the theory, methods, and expectations in my own field.

 

[Physics Monkey]

There is a lot to discuss here, and I really appreciate the attempt to cross the (unnecessary) boundaries between these two communities. Although there were a number of interesting points made, I will begin with my criticisms. I focus only on the quantum gravity aspects.

1. How can any review about string theory not mention the word "duality"? The review certainly mentions some examples of duality, but no explicit attention is given to this. This suggests to me a major category of results in string theory that string theorists believe are extremely important. Are these results judged not important or not relevant?

2. String theory contains GR as a special case. There is no mention of this fact as far as I can tell, or at least no mention of the way this classic result flows from the world sheet description. I think you can't call GR background independent and not give the same status to string theory. String theory contains and string theorists study all the interesting non-perturbative solutions mentioned near the bottom of page 3 on the left. Of course there is much to learn, but isn't string theory already as good as GR?

3. Related to 2, string theory definitely contains classical GR, but as far as I know this continues to be uncertain in loop quantum gravity. I know we discussed this issue relatively recently, but has any progress been made since then? Rovelli and others may believe strongly that the classical limit is right (or maybe not), but in string theory it pops out in a completely unambiguous way, so surely this dichotomy should have been mentioned? If the pros think we're almost there, then I'm fine with that, but not mentioning this issue while simultaneously insisting on the calling ads-cft a conjecture seems unfair to me.

4. Related to the end of 3, ads-cft may technically be a conjecture, but in my opinion this is disingenuous. Yes, the duality is not formally proven and some people have objections, but there is an enormous amount of evidence in its favor. Rovelli's review explicitly refers to ads-cft as not "addressing the real problem". I think that is an extremely unfair characterization. Ads-cft provides a complete non-perturbative definition of quantum gravity in certain asymptotic spacetimes with the right classical limit.

5. I think the review was right to accept the UV finiteness of strings, but I would have liked to have seen more about this issue and the related issue of "quantum geometry". What about T duality? What about topology change? What about singularity resolution?

I'd be happy to change my mind if I missed something in my reading, but right now I feel like a lot of important stuff was left out.

 

[marcus]

...
1. How can any review about string theory not mention the word "duality"? The review certainly mentions some examples of duality, but no explicit attention is given to this. This suggests to me a major category of results in string theory that string theorists believe are extremely important. Are these results judged not important or not relevant?
...
...
I'd be happy to change my mind if I missed something in my reading, but right now I feel like a lot of important stuff was left out.

The critical look explicitly refers to string dualities and certainly uses the word Look on page 4, first full paragraph.

I think it is misleading to term this brief 7-page critical look a "review". The review would, I guess, be the whole special issue of Foundations of Physics journal, which will be devoted to a retrospective "forty years of string theory".

Gerard 't Hooft took charge of compiling and editing this special issue of Foundations, and he gathered contributions from many people---mostly string theorists. I think he probably invited Carlo Rovelli specifically to give a critical look from an outsider's perspective. Certainly not what one usually considers to be a full review article!

Regarding this 7-page contribution by Rovelli, the question is not 'how complete is the review?' but 'are the criticisms well posed?'

But as for dualities, strong positive mention is explicitly made of them. You may have missed it in a hasty reading.

 

[Physics Monkey]

Fine, don't call it a review. Call it an assessment. I just needed a noun. Drawing attention to my nomenclature is an irrelevant semantic dodge since Rovelli does review many aspects of the string framework. Unless you or someone else wants to suggest that calling it or not calling it a review is actually an important issue?

Note that I didn't ask for completeness, I suggested that the assessment was missing major crucial pieces of the physics. There is a long way between missing major idea clusters (which I hope we agree would lead to less enlightened comparison) and missing details which no 7 page work could be expected to contain.

And you're right, I made a mistake. He does use the word duality once (in a different tense than I had searched for after not seeing it), but nothing is said about it! Or almost nothing, except that the relations are "beautiful" and difficult to evaluate the significance of. If missing that is hasty reading then so be it. Furthermore, the statements at the beginning of that same paragraph betray a certain prejudice about the way string theory is supposed to work. Maybe there are no "basic degrees of freedom", this is after all part of the message of dualities.

 

[marcus]

It seems to me that he took pains to be fair to the string approach---and more than that: kind, friendly, collegial. He had a lot of positive appreciation and praise for stringy achievements.

The question as I see it is whether this very brief critical outside assessment could contribute some value or usefulness to the broad review of string foundations and progress that Gerard 't Hooft and the other editors are preparing.

You may have seen other preprints of articles (by string theorists) contributed to this collection. What can the perspective of someone outside the field, working on a fundamentally different approach, add? What issues can he put in contrast that might not get such focused attention in the other papers?

Some of the invited contributions to that special issue of Foundations of Physics.
Giddings: http://arxiv.org/abs/1105.6359
Rovelli: http://arxiv.org/abs/1108.0868
Gubser: http://arxiv.org/abs/1103.3636

Other articles written for the issue, which may be included.
Balasubramanian: http://arxiv.org/abs/1107.2897
Rickles: http://arxiv.org/abs/1004.4491

 

[martinbn]

2. String theory contains GR as a special case.

How does it contain GR as a special case? I have always been curious to see that.

 

[unusualname]

This appears a very fair overview to me. Rovelli indicates that he will be assessing String Theory according to precise bounds at the beginning (vis a vis LQG), so dualities are not discussed because they are rather the (powerful) mathematical motivation for the theory, something which LQG doesn't (tediously) constantly appeal to.

Rather sneakily he does suggest that string theory might only fulfill the aims of its beginnings with Veneziano, in helping to explain hadron physics via improved QCD calculations

In any case he has the very strong case that low energy SUSY particles haven't been found yet, and ST conveniently can get around that and any other finding at the LHC.

Maybe both String Theory and LQG will end up as a branch of "toy" mathematics.

 

[tom.stoer]

The weak point in the article could be that Rovelli compares strings with LQG. The restriction to quantum gravity and the focus on one single theory of quantum gravity could very well miss the essential nature of string theory.

Let's assume for a moment that we have a rather nice effective theory for strong interactions, e.g. chiral perturbation theory. Now let's assume that for some reason we have not yet identified the SU(3) color-gauge theory for strong interactions, but a lot of other gauge theories (not relevant for strong interactions). Now let's compare gauge theory with chiral perturbation theory: our judgement would be that chiral perturbation theory wins agains gauge theory regarding the description of strong interaction ... what a misjudgment.

String theory could very well be a framework for constructing consistent theories. Perhaps one should compare string theory with spin networks; here "spin networks" would mean "the set of all spin network theories constructed from arbitrary Lie groups, quantum groups, affine Lie groups, ..."

Rearding many details and weak points of string theory a share Rovelli's opinion

 

[unusualname]

The weak point in the article could be that Rovelli compares strings with LQG. The restriction to quantum gravity and the focus on one single theory of quantum gravity could very well miss the essential nature of string theory.

Let's assume for a moment that we have a rather nice effective theory for strong interactions, e.g. chiral perturbation theory. Now let's assume that for some reason we have not yet identified the SU(3) color-gauge theory for strong interactions, but a lot of other gauge theories (not relevant for strong interactions). Now let's compare gauge theory with chiral perturbation theory: our judgement would be that chiral perturbation theory wins agains gauge theory regarding the description of strong interaction ... what a misjudgment.

String theory could very well be a framework for constructing consistent theories. Perhaps one should compare string theory with spin networks; here "spin networks" would mean "the set of all spin network theories constructed from arbitrary Lie groups, quantum groups, affine Lie groups, ..."

Rearding many details and weak points of string theory a share Rovelli's opinion

But he clearly states that the ONLY reason he agreed to write the article was to compare ST to LQG, so he is not arguing against the fact that ST might be applicable to the Standard Model of particles better than LQG, but rather that ST is fundamentally not convincingly physically motivated, perhaps because it is trying to do too much.

Anyway, I think its a brave article in these times, and well worth a read.

 

[tom.stoer]

Anyway, I think its a brave article in these times, and well worth a read.

Yes!

 

[Ben Niehoff]

How does it contain GR as a special case? I have always been curious to see that.

This is a standard textbook result. One obtains the Einstein equations for the background metric by conformal symmetry on the world sheet (i.e., from the vanishing of beta functions for the worldsheet CFT). It should be discussed in Becker, Becker, Schwarz, and most any other string theory textbook.

 

[Fra]

What I like about most Rovelli's writings is that he has a reasonably clear and honest writing style, which also means it's easy to see when you disagree.

Knowing about Rovelli's logic and views since before, when I read the paper it provides no constructive new views on ST, to me it rather just confirms what really is Rovelli's stance.

I have put forward my objections to Rovelli's reasoning before, and don't want to repeat myself, since what rovelli writes is stuff I've read before.

But shortly, if I may be so bold to critique Rovellis thinking, I again must say that some of Rovelli's critique against ST seems (to me) be rooted in his own understanding of measurement theory, inferences and what a theory is. (Needless to say I disagree with his viewe). The reason I think that some parts are unfair critique is not because I like or advocate ST, it's because some of that critique can be closely applied to my own personal ideas. While I see that I'm no one compare to Rovelli I feel quite confident that something just isn't right about his application of "measurement theory" on the "observer invariants".

The reason for difficulty of finding/understanding an observer invariant measurement theory is IMO much deeper that what Rovelli's stance seems to allow. IMHO, clearly the "background" comes with hte observer. Rovelli's way of doing away with the observer simply does not make sense to me, no matter how stupid that may make me look.

Maybe there are no "basic degrees of freedom", this is after all part of the message of dualities.

I fully agree. But in a general sense (et give or take ST). Rovelli doesn't seem to consider this an option. This is one aspect of all the things I mentioned above. IMHO. degrees of freedom (or I prefer to say complexions because the continuum is not an a priori), are INFERRED, and inference requires a context(background; however not a static one). This is why there is a deep problem to even define the notion of DOF in a proper inference (which is to me what should take place in a generalizedr measurement theory).

Some of this critique applies to ST as well, but it apparently applies even stronger to Rovelli's/LQG logic.

/Fredrik

 

[martinbn]

This is a standard textbook result. One obtains the Einstein equations for the background metric by conformal symmetry on the world sheet (i.e., from the vanishing of beta functions for the worldsheet CFT). It should be discussed in Becker, Becker, Schwarz, and most any other string theory textbook.

That is the answer I was given before, but what I found in the textbooks was: First part of the book covers the theory on flat ten dimensional space-time. When one wants to develop the theory on a different manifold one has to work with a Ricci flat ten dimensional manifold. Surely that is not the same as contains GR as a spatial case or classical limit.

 

[Ben Niehoff]

That is the answer I was given before, but what I found in the textbooks was: First part of the book covers the theory on flat ten dimensional space-time. When one wants to develop the theory on a different manifold one has to work with a Ricci flat ten dimensional manifold. Surely that is not the same as contains GR as a spatial case or classical limit.

A Ricci-flat manifold is an Einstein manifold, isn't it? And it's not just that one must work in a Ricci-flat background...it's also that one obtains an action for the background fields, and that action is the Einstein-Hilbert action coupled to additional matter fields.

To obtain the Einstein-Hilbert action coupled to matter fields in 4 dimensions, all you have to do is compactify somehow. There are lots of ways to do that.

See also Clifford Johnson's book, D-Branes. One can use stacks of D-branes to create all sorts of background geometries, including the analogues of Schwarzschild, Kerr, Reissner-Nordstrom, etc., in all dimensions from 2 to 11.

 

[Fra]

This is how Rovelli objects to the quest for a full B/I independent string theory:

The way this fundamental issue is addressed in string theory is often indirect. For instance, attempts are made to describe the bulk quantum geometry of spacetime by using the ADS-CFT conjecture, thus trying to describe what we do not know (quantum gravity) in terms of conceptual tools that we control (flat-space quantum field theory on the boundary).

instead of addressing the real problem,which is to learn how to do physics where background spacetime plays no role, the strategy is to try to circumvent the problem, bringing back the calculations to the familiar pre-general-relativistic conceptual framework.

There are plenty of fair objections to ST, but the above seems to be a central objection of Rovelli, but I have to say that I can actually see a good logic behind the struggle that goes on in ST. And it can be partly understood in a way that has nothing to do with ST specifically, but rather that would be common to any framework that might aim at considering evolving theories (which is at least ONE possible route in ST, but there are others).

IMO, the background unavoidably comes once you Pick a real observer. This is the observer doing ALL inferences. The observing system is also physical hosting and encoding a theory. In the general case the background is more than JUST spacetime, but the argument still holds for spacetime only if we insist on that B/I definition.

The "indirect" adressing Rovelli objects to IMO, can be understood like this: The only way to measure or assess one theory, is from the point of view of another theory. Ie. The only way to infer background independence of a certain class of theories, you need another theory. In other words, it must actually be true that background independence paradoxally IS background dependent. The exceptions with GR - is since it's a CLASSICAL theory. I think it's a mistake to extrapolate this non-inference (from a realist theory) to the quantum domain. So the problems seems to actually BE how to understand a populating of interacting theories (backgrounds in the sub-problem). The quest for fundamental timeless eternal DOF's that are observer invariant seems to be a extrapolation from classical physics, where we do not have to worry about how one observer in detail infers(measures) something, and how they compare the result, because in the classical world this is much more trivial.

The asymptotic correspondence of a boundary can be understood as how an observer at infinity would "infer" or assess the physics that's inside the bound. The only objection I have to this is not that of Rovelli but rather that the asymptotics does not seem to qualify as a general realistic observer. Asymptotics work for special cases, such as for assessing microscopic black holes Maybe, but it seems to be a special case only, because a finite observer can never access this asymptotic information in reality - and thus not make any inferences. But rovelli's critique seems to be quite different, he seems to address not such details but the general idea of two different theories describing each other. I think it does make sense in a very general sense (which you can appreciate without ST), it seems he does not?

I think maybe some of this roots also in the obsession with falsifiability of theories. But it could very well be that the understanding of what a theory is, is needed. Again, I know a lot of people has written that this is ST making excuses for this and that, but I've given this this good thought outside ST, and there are actually good rational thinking in this. This is interesting because it does touches not only the foundations of physics, but also of science.

/Fredrik

 

[martinbn]

A Ricci-flat manifold is an Einstein manifold, isn't it? And it's not just that one must work in a Ricci-flat background...it's also that one obtains an action for the background fields, and that action is the Einstein-Hilbert action coupled to additional matter fields.

To obtain the Einstein-Hilbert action coupled to matter fields in 4 dimensions, all you have to do is compactify somehow. There are lots of ways to do that.

See also Clifford Johnson's book, D-Branes. One can use stacks of D-branes to create all sorts of background geometries, including the analogues of Schwarzschild, Kerr, Reissner-Nordstrom, etc., in all dimensions from 2 to 11.

Yes, but there is a difference between having a theory, which reduces to GR and being able to beging to build the theory only if you take a fixed Ricci flat manifold as a background.

 

[Ben Niehoff]

Yes, but there is a difference between having a theory, which reduces to GR and being able to beging to build the theory only if you take a fixed Ricci flat manifold as a background.

This is becoming kind of a tangential discussion, but anyway...

Perhaps you have misunderstood. The whole point is that string theory demands GR as a consistency condition. Kind of like a Ward identity. In order for any relativistic quantum theory of 1-dimensional extended objects to be consistent, it must be on an Einstein background in 10 (with SUSY) or 26 (with bosonic modes only) dimensions.

I'm not sure where you got the qualifier "fixed" from. The background metric G is a coherent state of string modes. The background itself is built out of a field of virtual closed strings being exchanged.

In QED one solves the hydrogen atom by assuming a classical background (i.e., a 1/r potential) and looking at small perturbations from it (i.e., we solve the Dirac equation in the given background). Does this mean that QED only works for fixed backgrounds? No, if we were to look at the full interacting theory we should be able to find bound states of protons and electrons and the 1/r potential would come out as a low-energy solution to the theory rather than a background we put in by hand. But that is a very difficult calculation to do, as all our perturbative techniques are designed to attack scattering problems that do not result in bound states.

The situation is similar in string theory. We know that in the full interacting theory at high energy, the "background" one would get is not even describable by traditional geometry. In some regimes it may be some kind of non-commutative geometry. In other regimes, who knows. This is a very difficult problem. But we do know that at low energies, the theory gives us things that look like geometry, and those geometries are required to solve the Einstein equations (with some matter fields). So the easiest thing to do is find a classical background, and then look at what happens with strings propagating on that background.

 

[martinbn]

This is becoming kind of a tangential discussion, but anyway...

Yes, I am sorry about that.

Perhaps you have misunderstood. The whole point is that string theory demands GR as a consistency condition. Kind of like a Ward identity. In order for any relativistic quantum theory of 1-dimensional extended objects to be consistent, it must be on an Einstein background in 10 (with SUSY) or 26 (with bosonic modes only) dimensions.

That is how I understood it. The consistency condition has to be imposed before we have that theory. When I hear that ST contains GR, I expect to see the theory and from it as a classical limit to derive GT, but I didn't see that. What i found was, we want to quantise strings in not necessarily Minkowski spacetime, and the only spacetimes we can do it on is Ricci flat. Perhaps I need look more into it.

I'm not sure where you got the qualifier "fixed" from. The background metric G is a coherent state of string modes. The background itself is built out of a field of virtual closed strings being exchanged.

Most likely I didn't understand something. But I got it out of the textbooks.

In QED one solves the hydrogen atom by assuming a classical background (i.e., a 1/r potential) and looking at small perturbations from it (i.e., we solve the Dirac equation in the given background). Does this mean that QED only works for fixed backgrounds? No, if we were to look at the full interacting theory we should be able to find bound states of protons and electrons and the 1/r potential would come out as a low-energy solution to the theory rather than a background we put in by hand. But that is a very difficult calculation to do, as all our perturbative techniques are designed to attack scattering problems that do not result in bound states.

That is different. I have no problem with this, making simplifying assumptions when solving specific problems.

The situation is similar in string theory. We know that in the full interacting theory at high energy, the "background" one would get is not even describable by traditional geometry. In some regimes it may be some kind of non-commutative geometry. In other regimes, who knows. This is a very difficult problem. But we do know that at low energies, the theory gives us things that look like geometry, and those geometries are required to solve the Einstein equations (with some matter fields). So the easiest thing to do is find a classical background, and then look at what happens with strings propagating on that background.

This sounds like what I would like to see, but the books gave me a different impression.

 

[genneth]

The situation is similar in string theory. We know that in the full interacting theory at high energy, the "background" one would get is not even describable by traditional geometry. In some regimes it may be some kind of non-commutative geometry. In other regimes, who knows. This is a very difficult problem. But we do know that at low energies, the theory gives us things that look like geometry, and those geometries are required to solve the Einstein equations (with some matter fields). So the easiest thing to do is find a classical background, and then look at what happens with strings propagating on that background.

Relativists (used to?) have trouble with this picture because it wasn't clear why flat metrics should be preferential --- many took/take background independence to mean that all metrics should be considered equally. The particle physics tradition (of which string theory must be regarded as being born from) has always been about perturbation analysis of some sort --- thus the focus on vacuums and excitation on top.

The thing is, from LQG I actually think the relativists might have finally found something "special" about flat backgrounds which distinguishes them (in the quantum regime) from others --- the so-call Ditt invariance; i.e. when you "refine" the combinatorial structure in LQG flat metrics are fixed points of this procedure, and reflects the fact that LQG works by "gluing" flat simplices together, a la Regge.

It's worth (for relativists) to think deeply about the string view point. As various string theorists point out, the fact that GR is in string theory is a "trivial" consequence --- the whole edifice is designed to give weak-field GR! One day, we might even understand that, like gauge theories, string theory is an essentially unique (i.e. self-consistent) extension of QFT to include gravitons, and so necessarily reproduces the correct low energy picture, but one which is not incompatible with a more "covariant" point of view. For example, high energy scattering in QCD is perfectly reasonably calculated by considering perturbations to an empty vacuum, but one also reasonably concludes that in other regimes it is sensible to use a lattice method.

 

[suprised]

It's worth (for relativists) to think deeply about the string view point. As various string theorists point out, the fact that GR is in string theory is a "trivial" consequence --- the whole edifice is designed to give weak-field GR!

Originally - but more recently one has seen glimpses of non-geometrical regimes and begins to understand "space-time geometry beyond space-time". For example, near singularities or more generally in regions of large curvature where notions of classical geometry break down. Certainly string theory is much more generally defined than in terms of smooth manifolds etc.

One day, we might even understand that, like gauge theories, string theory is an essentially unique (i.e. self-consistent) extension of QFT to include gravitons, and so necessarily reproduces the correct low energy picture, but one which is not incompatible with a more "covariant" point of view. For example, high energy scattering in QCD is perfectly reasonably calculated by considering perturbations to an empty vacuum, but one also reasonably concludes that in other regimes it is sensible to use a lattice method.

I guess this is a fairy reasonable point of view: as formulated today, string theory is more akin to lagrangian QCD, and LQG (ie: whatever formulation of the many approaches that were proposed that will ultimately make sense) is more akin to lattice QCD.

 

[Physics Monkey]

I'm not claiming that Rovelli intentionally treated string theory unfairly, but I do think a case can be made for the claim that Rovelli missed some important points. Of course, that in itself is part of the point of an external point of view.

I'm not advocating for any funding policies or grand research agendas or trying to determine the fate of either theory. I am an outsider to both, and I like to learn about both.

However, as I see it, string theory is clearly ahead as a theory of quantum gravity.
1. It contains GR.
2. It is finite and sensible in the UV.
3. It makes sense of topology change and singularity resolution.
4. It has a clear physical picture of Planck or string scale "graininess" coming from strings, branes, and duality
5. It provides, via holographic duality, the first complete definition of quantum gravity in certain asymptotic spaces.
6. It has understood certain black hole microstates.

I would rate LQG as follows:
1. Close, but I'm not sure how close
2. Sure, this seems built in
3. Sure (I'm thinking of cosmology as an example here)
4. Sure, also seems built in
5. Little known
6. Yes, but with some limits and conditions that I think are not understood

One of the things which most impresses me about LQG is the way they make progress without the aid of supersymmetry. I feel like in some ways I can trust the results of the LQG community to be a better source of inspiration for my own work.

Overall, it's a complicated and intriguing picture, but I do think that as far as pure quantum gravity is concerned, string theory paints a more complete story at the present.

 

[atyy]

However, as I see it, string theory is clearly ahead as a theory of quantum gravity. ...
2. It is finite and sensible in the UV. ...

I would rate LQG as follows: ...
2. Sure, this seems built in

Although LQG is strictly speaking, UV finite, it has other potential divergences. We've had some discussion at https://www.physicsforums.com/showthread.php?t=517464.

 

[Ben Niehoff]

That is how I understood it. The consistency condition has to be imposed before we have that theory. When I hear that ST contains GR, I expect to see the theory and from it as a classical limit to derive GT, but I didn't see that. What i found was, we want to quantise strings in not necessarily Minkowski spacetime, and the only spacetimes we can do it on is Ricci flat. Perhaps I need look more into it.

<snip about various regimes in string theory>

This sounds like what I would like to see, but the books gave me a different impression.

I think the textbooks give the wrong impression for a few reasons. First is that they are textbooks, so they start with the simplest things and move from there. Second, they tend to be arranged in the order things were discovered chronologically, more or less.

String theory wasn't originally intended to be a quantum theory of gravity. It was intended as a way to attack QCD. And as such, it was originally formulated against a flat background. But what happens if you follow your nose is that the theory starts telling you things about itself:

1. Hey, I'm only consistent in 26 dimensions (10 if you put in fermions)!

2. My ground state is a tachyon. Whoops. But you can get rid of it if you put in fermions and project onto a special sector of the Hilbert space.

3. My massless states include a spin 2 particle! Hey, maybe there's gravity here...

4. If you try to put me in a curved background, it had better be a solution to Einstein's equations.

I think a stronger way to say string theory contains gravity, however, is this: If we want to know about string theory at low energy, we should look at its low-energy excitations. The string has an infinite tower of possible excitations, each with greater mass than before. So if we ignore all the massive ones and just look at the massless excitations, we get (for the superstring): a metric field, a 2-form potential, a dilaton, and the RR p-form potentials, plus all of their superpartners.

We can then ask, what is the low-energy effective action for these fields, consistent with all the supersymmetries relating them? This question takes some non-trivial work to answer; you have to compute some string diagrams for closed string exchange. But the answer you get is N=2 supergravity in 10 dimensions -- two different versions, types IIA and IIB, depending on whether you have odd or even RR p-form potentials. The other string theories have N=1 SUSY and give you N=1 supergravities (there are many possible supergravities in 10 dimensions...if I remember correctly, string theory actually gives you all of them).

This process is analogous to computing some tree diagrams in QED and getting the classical 1/r potential.

 

[Fra]

The situation is similar in string theory. We know that in the full interacting theory at high energy, the "background" one would get is not even describable by traditional geometry. In some regimes it may be some kind of non-commutative geometry. In other regimes, who knows. This is a very difficult problem. But we do know that at low energies, the theory gives us things that look like geometry, and those geometries are required to solve the Einstein equations (with some matter fields). So the easiest thing to do is find a classical background, and then look at what happens with strings propagating on that background.

Forgive a possibly ignorant question but, wouldn't it be fair to say that there is a difference between

1) showing that - as you say - the "full interacting theory" - including a background evolution - does indeeed always yield the desired result.

2) saying that since the consistency constraint - during the QUEST/construction of the full theory - is that the background MUST have a certain symmetry? And that the "constraint" of the background during the manual selection process when working in fixed BG is a trick needed just until the full theory is in place.

But I mean after all, the "full interacting theory" isn't yet found? what what happens to argument (2) if it does not exists? It seems to rely on that the full interacting theory - constructed as per he string logic - does exist at all?

I mean, you refer to certain properties as following more or less from it's constructing principles, but do we really know that the construction (as per the stated constructing principles) will work and actually result in a full theory?

or do you think this an unreasonable point? There is notthing wrong but an insider having confidence in a reasearch direction, but still there is a difference between conjecture and established result. I'm not sure if this was martinb's point or not but I 'll throw it out.

/Fredrik

 

[Ben Niehoff]

We don't yet have a full, non-perturbative definition of string theory; this is an open field of research. But note that we don't have a full, non-perturbative definition of QCD either (although QCD benefits from its perturbative calculations corresponding with experiment).

So yes, there is a bit of exploring unknown territory involved. But we are able to probe bits and pieces of it. We know that perturbative string theory is UV-finite, and we are able to conclude a few non-perturbative things (c.f. D-branes). The full, interacting theory is believed to be "string field theory", which is what you get when you second-quantize the strings themselves. This is an extraordinarily difficult subject.

At any rate, to see gravity pop out most easily, see my most recent post to Martin above. The best way is to look at low-energy excitations (i.e. massless modes), compute some string diagrams, and obtain an effective action. The effective action turns out to be supergravity in 10 dimensions. So we know that whatever string theory "really" is, its low-energy limit is 10-dimensional supergravity.

2) saying that since the consistency constraint - during the QUEST/construction of the full theory - is that the background MUST have a certain symmetry? And that the "constraint" of the background during the manual selection process when working in fixed BG is a trick needed just until the full theory is in place.

I have to add, I think this attitude is somewhat asinine. String theory isn't "background independent" because we have to "manually select" a background to satisfy the "consistency constraint"? It makes me wonder, what sort of concept of "background independence" would satisfy a person who thinks this way.

Think about it. The consistency constraint is Einstein's equations. So sure, we have to choose a background, but it can be any background whatsoever that satisfies Einstein's equations.

This is the same amount of "background independence" that is contained in classical GR! After all, you have to choose a background manifold, and it can be any manifold you like, as long as it satisfies Einstein's equations...

To say, therefore, that string theory is not "background independent" is quibbling over semantics. I don't really get it.

 

[Fra]

Thanks for the comment.

I just wanted to raise that question and see your input, as I suspected that maybe it was part of martinb's point? Personally my view on the B/I issue is different. I do not share the Rovelli style objections, mine are different. See below.

We don't yet have a full, non-perturbative definition of string theory; this is an open field of research. But note that we don't have a full, non-perturbative definition of QCD either (although QCD benefits from its perturbative calculations corresponding with experiment).

There is nothing wrong with perturbations seen as a mathematical solving technique. But the "perturbations" we are talking about here are IMO of more profound nature(or Is it? in fact ones opinon of this, reveaels some of the attitude I address below! what's your view), so it's not the same.

What I mean is that, either you see perturbation theory as a mathematical thing, void of physics. Or you understand it in the context of a renormalization, where suddently the perturbations get physical meaning. Then it's physics, and not just taylor expansions.

Also, since ST aims to be a unificaation theory, even my expectations of what to expect are way higher. What other theories get away with, might not be accepted for a unifying theory. QCD formulation are entirely dependent on a background spacetime. So clearly if we mess that up, the entire SM model will too. So in this sense, ST predictions of all kinds of unobserved things are not unreasonable. It all depends on wether the background can be predicted, rather than just selected - or more likely that a naviation principle is found for evolving the background. The "inference" of QCD, is made from a stable backdrop like a laboratory frame.

But that said, I think that the still lacking GUT is a sign of a lack of an "inside view" like is needed for a cosmological measurement theory (meaning there IS no stable background; the infering system is rather floating in an unknown environment).

The full, interacting theory is believed to be "string field theory", which is what you get when you second-quantize the strings themselves. This is an extraordinarily difficult subject.

Yes that's true. I didn't expect instant noodles, just wanted to suggest that some of the soundness of reasoning in the perturbative picture, might depend on conjectures about the existence of the full theory.

To say, therefore, that string theory is not "background independent" is quibbling over semantics. I don't really get it.

Actually my own, view on this issue is a little different that I think both ST view and Rovellis' view.w

I do think that some arguments from say LQG folks (ie rovelli) are not quite right, because their view of B/I has two problems I object to
1) it's a too narrow definition of background, from my point of inferencial theories, it is incoherent to give special treatment to some information and ban fixing it; when other parts are allowed to be fixed. In my view, ANY structure that the inferneces relies on is a background, and thus part of the observing system.

2) The rational argument for the entire B/I thing as well as the constructing principles of relativity is that all observers (and thus choices of reference frames associated to it) must be equally valid for making inferences of physics: still there are two ways to see this, either as observer invariance as a constraint, or as observer democracy.

Rovelli's view on this is IMO quite "clear", which btw doesn't mean I agree with it.

But I have to admit that I never quite understood a coherent ST reasoning in terms of the more general background independence (referring to ANY context, not JUST a spacetime reference frame). And since the ST Background is not JUST the simple 4D background, but rather a higher dimensional background, including some compactificataion - this at least MIGHT qualify as something that COULD encode the more "general" background I refer to...

(It simply seems (as far as I can tell from reading what string theorist say) an open problem in ST, that moreover different string people have different opinons on. )

... but THEN the question immediately appears: what reason do we have to think that the model bult from the string conjecture really is a theory of theory? This is my objection. And I think the soundness of the constructing principles, does depend on how you view this. For me at least it's more than semantics.

/Fredrik

 

[Fra]

I forgot the conclusion:

And since the ST Background is not JUST the simple 4D background, but rather a higher dimensional background, including some compactificataion - this at least MIGHT qualify as something that COULD encode the more "general" background I refer to...

If we for the sake of argument assumes this picture, then what "background independence" would mean (for me) is exactly understood as a form of background democracy.

But that picture makes sense, only if what we may call the "democratic process" is understood. This means how to understand how two backgrounds can interact, and how their interactions evolve the background Beyond the $\eta / h$ split.

And if we characterise string theory this way (using my abstractions that are admiddetly not how string theorists normally think of their things) then part of what is missing in string theory is an understanding of the "democracti process". Of course this is also related to the landscape problem, which also seems to be of debate also withing ST - ie how to "handle it".

So the background space made up of interacting strings might be seen as the result of a democratic negotiation, but this exact process is not understood. And since this is how I personally "make sense" of B/I in the deeper sense, the consistency of the claim of background democracy depends on at least some kind of understanding or conjecture about this process.

/Fredrik

 

[Ben Niehoff]

Yes that's true. I didn't expect instant noodles, just wanted to suggest that some of the soundness of reasoning in the perturbative picture, might depend on conjectures about the existence of the full theory.

The perturbative picture is quite well-defined. But then there is always the question of when non-perturbative effects become important. And then one can ask, "Non-perturbative effects of what?" That is to say, we're not quite sure what the full theory is, exactly, and whether it is well-defined in a non-perturbative sense.

But I brought up QCD because the same questions are there as to whether QCD exists, rigorously speaking. In fact, there's a million dollar prize on the line for it.

So if it troubles you that we have not demonstrated rigorously that a "full version" of string theory exists, then you should be equally troubled by QCD and the whole Standard Model. I don't think your concern is an issue specific to string theory.


This is about all I can respond to, because I can't make out exactly what you are trying to get at with the rest of your post. I am not a regular reader of Rovelli, so if you are making references to his terminology I really have no idea what you're saying. At any rate, from what you've written, I don't understand what your idea of "background" is, nor your idea of "background independence".

 

[Fra]

then you should be equally troubled by QCD and the whole Standard Model. I don't think your concern is an issue specific to string theory.

You are partly right on this, my issues applies to other theories as well. But OTOH, the standards for a unification inferencial style theory that I seek, should be higher, and the arguemtns for SM are quite different. SM as it stands, doesn't even make sense unless we have a stable background spacetime or labframe. So it's obvious upfront that there are incompleteness there. But this is one of the reason we seek a unified theory that can be formulated in more general terms. So I think - for good reasons - I ask much more out of ST than I do out of QCD.

But, much thanks for your response. Even though I wasn't able convey that thing about background democracy vs background independence, we still got one step.

/Fredrik

 

[haushofer]

I'm a complete n00b when it's about LQG, but in the review Rovelli states in section III that the UV-finiteness of LQG is straightforward, and gives a short explanation. Is it really that clear that LQG is UV-finite?

 

[suprised]

Well whenever you have a cutoff scale things will be finite. The question is whether the quantities you compute depend on this cutoff in a bad way or not; conventional QG is non-renormalizable, so even if you put a cutoff, the theory depends on it in a bad way, ie. you need to specify an infinite amount of data in order to make sense of scattering amplitudes. I am not sure how LQG deals with this problem; in ordinary QFT, putting a non-renormalizable theory on a discrete lattice and thereby regularizing divergences by brute force, does not really solve this problem. Perhaps someone else can explain whether/how in LQG higher order quantum corrections are rendered harmless, in this sense.

 

[haushofer]

But how does one concretely calculate for instance interactions in LQG if spacetime is discrete? How are e.g. integrals defined in the first place (without worrying about cutoffs)?

To which extend is one able to do real calculations in LQG and check this statement explicitly for explicit cases?

 

[atyy]

UV usually requires a metric to be defined. Since there is no metric, there are no UV divergences (if I understand Rovelli's use of language). There are nonetheless potential divergences analogous to UV divergences https://www.physicsforums.com/showthread.php?t=517464

 

[suprised]

I guess LQG is in the "wrong phase" for doing such calculations. Because such calculations need a background around which one perturbs, one would first need to develop an appropriate framework to even formulate the problem. It seems strings can provide the appropriate framework for this kind of problems. It is hard to see how one could avoid the geometry of riemann surfaces (ie their moduli spaces) if one wants to have unitary scattering amplitudes. This is an extra ingredient that goes beyond usual QFT.

If in such a "broken" phase LQG would just reproduce gravity with a cutoff, then most likely it would not be consistent. Or perhaps it would be equivalent to strings (which however would imply extra degrees of freedom, so it is not standard gravity).

Again, the issue is not just finiteness. It is also about consistent, unitary scattering amplitudes.

 

[marcus]

I guess LQG is in the "wrong phase" for doing such calculations. Because such calculations need a background around which one perturbs, one would first need to develop an appropriate framework to even formulate the problem...
... scattering amplitudes.

But one can introduce a specific background as a context for calculating scattering amplitudes.
Nothing says that in a background independent theory one cannot specify a given background for some particular purpose.

In Lqg this is done by fixing the quantum state of the boundary geometry, and then some n-point function calculations have been made. This has some references:
http://arxiv.org/abs/1105.0566