Why I am REALLY disappointed about string theory

[mitchell porter]

The only thing I found with "Fivebranes and knots" was this August 17th talk:

http://online.kitp.ucsb.edu/online/duallang_m10/witten2/

Is there anything else?

It's work in progress by Witten. Partly it descends from hep-th/9912123 but there are many other ingredients. For the 6D (2,0) SCFT which is a worldvolume theory for parallel M5-branes (and which only shows up at about 88 minutes in the talk), you could try hep-th/0608014, section 4.2, for an introduction.

An interesting basic fact about M-branes is that you can have an M2-brane in the shape of a cylinder stretched between two M5-branes. It's analogous to an open string stretched between D-branes in string theory. But the M2 cylinder ends on a loop in the M5-brane, so from within the M5-brane, the ends of interacting M2-branes look like closed strings inside the M5!

Some weeks ago I asked regarding string field theory. Something more to say about that?

Last month, in comment #87 in this thread, I said Witten invented string field theory, which is wrong. It goes back to Kaku and Kikkawa in 1974.

 

[tom.stoer]

Just a last note on this


From my perspective, there is no difference between the two possibilities you describe.

...

"What the observer knows, is indistinguishable from what hte observer IS"

Just to clarify: inventing QCD means (to us humans) to learn more about the strong interaction; so the perspective of the observer changes. But it does not mean that the strong interaction itself changes. It's only that we understand more about it. Strong interaction is the same before and after the appearance of QCD in our physical theories.

It's like prime numbers: A number which is prime is prime even if we do not know that this number is prime. Calculating its prime factors changes our knowledge, but not the number itself.

What does that mean to string theory? It means that we are still looking for one unifying framework which harmonizes the different patches of the theory (just like the different low-energy effective theories for QCD). The framework of string theory (still to be identified) will then reflect our current knowledge regarding the different interactions we observe in nature. If this knowledge increases it may become necessary to change or enlarge this framework again. Therefore it is of course necessary to go through this mess of different formulations, symmetry breaking, vacua, low-energy descriptions, discussing different patches within M-theory etc. Nevertheless one framework to address all these questions is preferred over the situation as of today.

So again: for me there is no (known) PHYSICAL reason which prevents us from identifying this framework; it's our limited knowledge, or limited mathematical capabilities, or perhaps missing genius (a la Einstein). Not being able to identify QCD over a couple of decades was due to the limited knowledge, not due to PHYSICAL principles of the strong interactions.

 

[Fra]

Just to clarify: inventing QCD means (to us humans) to learn more about the strong interaction; so the perspective of the observer changes. But it does not mean that the strong interaction itself changes. It's only that we understand more about it. Strong interaction is the same before and after the appearance of QCD in our physical theories.

I understand and I agree you are right of course! I suspected you'd respond with this, it's hard to describe properly and be brief at the same time.

What I mean is this: The implication and difference "law" makes, is only when you consider the action of the system that encodes it.

I do not suggest that human understanding (information coded in human brain) causes the strong or weak or any other interaction to change! What I DO suggest is that the "knowledge" a quark, proton or electron have (ie what's encoded in the microstructure of the particle with given mass/energy etc) about physical interactions DOES actually change the interactions it participates in. This is the type of reasoning I expect to explain why certain interactions are indistinguishable at say different energy scales or, why only charged particles are deflected in an electrial field without beeing decomposed or destabilised.

The human analogy would take into account the action of the human. And indeed, this differes. When the scientists has a certain view of law; it surely reveals itself in the questions he asks, the experiments he designs. When his understanding has changed, so does his further questions and experimental designs.

So again: for me there is no (known) PHYSICAL reason which prevents us from identifying this framework; it's our limited knowledge, or limited mathematical capabilities, or perhaps missing genius (a la Einstein).

I see two domains where this makes a different. Cosomology - here human based knowledge is still tiny and physical truncations of information are unavoidable. So we really need to ask ourselves what we MEAN by say probabilities on cosmo level? Or states of the universe?

The other thing does affec the action of the microstructure of matter,and it's unification to large scale physics is that the scaling of interactions might be hard to understand if we insist timeless eternal fixed laws. After all, we still lack a GUT - this is one aread where I think this does matter. The external view that we get, comes with a lot of distinctions that are PROBABLY non-physical to the insiders in extreme high energy itneractions, and it we can understand how "physical law" scales properly, I think it will be easier to understand!

Not being able to identify QCD over a couple of decades was due to the limited knowledge, not due to PHYSICAL principles of the strong interactions.

Yes fully agreed of course. Maybe I overstated the implications of my view to the practical things. I certainly think that we humans can find such a framework for ST. I'm not really defending ST. I think the diversity in ST, is non-physical anyway. I just defended some traits of it.

I just think it's a guiding principle in general to seek for these structural realist eternal laws is wrong. I fully agree that we can and will find such things, I just say that they are merely effective and evolving. I think our learning will be more efficient if we have the right guiding principles.

/Fredrik

 

[tom.stoer]

OK, so let's come back to the main issue.

Suppose I am a brilliant, young physicists with the potential to identify the very foundations of string theory, the unifying framework (honestly: I am neither young nor brilliant). Suppose I have the chance to ask other physicists (including you) regarding the most promising research direction within string theory and regarding my future work.

What is your advice?

 

[Fra]

OK, so let's come back to the main issue.

Suppose I am a brilliant, young physicists with the potential to identify the very foundations of string theory, the unifying framework (honestly: I am neither young nor brilliant). Suppose I have the chance to ask other physicists (including you) regarding the most promising research direction within string theory and regarding my future work.

What is your advice?

I'm not at all qualified to answer to specifics of ST, if the premise of the question is to stick with ST.

I guess I would just encourage critical thinking and making your own assessements, and ask yourself wether ST really IS the only option?

What I personally think is the most interesting reaserch direction is neither within string theory, nor necessarily good advice if you want someone else to pay for your work, then you also need to look at the commercial and political aspects. (Carreer advice is a completely different question, and I don't think that's what we dicsuss here).

The only link I personally see to ST; is a reconstruction which is a completely different way of thinking - but it has similarities - where the "strings" may emerge as the simplest possible continuum structures in the large complexity limit. I actually associate the "string" to a "probability distribution" in the continuum limit of a discretely indexed string with discrete amplitudes, where each such distribution has a defined complexity. The full continuum string is not existing, it's rather discrete. IF that would work, it might in the end either provide an explanation and understanding to some of the assumptions of ST. Why strings, why the string action (should be a form of minimum divergence), but it requires non-commutative structures, so it would rather have to be different sets of discrete distributions that are related, what about the landscape etc. But it might as well show that string theory (seens as an inference model; which is what I think is the way to do) is simply wrong, maybe the string action is wrong, maybe something else is wrong - but then the right form should be found. That's impossible to tell at this point. In any way, it seems to me that IF ST is to make sense to ME, then it will also just be an effective model. In particular are the strings and branes not fundamental. The more general case would I envision be so different that it would be just silly to even call it string theory or m-theory.

My confidence in this direction I've just acquired over time. I really do listen and read what the experts think and there are some excellent ideas that tangent to this. But there are only some papers that sniff this. It's still highly undeveloped thinking and controversial. There simply is no group to join I'm aware of.

Edit: the "scaling of law" I mention is not just some regular renormalization. It's different, as it also contains evolutionary elements. The scaling is not cleanly separable from evolution. Therefore, do I not believe in objective deterministic renormalization rules. That still has too much strucutral realism in it. I think renormalization still await another revolution where it can be understood at an even deeper level. The scaling of an observer and thus law is not just mathematics, I think it's a physical process.

/Fredrik

 

[suprised]

it is exactly this, namely that up to now nobody is able to explain what string theory fundamentally IS.

No one knows, but there are always speculative answers and this is a rich field for bullgarbageting.

Tongue-in-the-cheek answer: this big blob of theories that one sees to emerge ist just the set of consistent quantum theories that include gravity. And "string theory" is just the proper way to parametrize it in special regions, analogous to "gauge theory" (if one decouples gravity). The question about a fundamental theory of strings would be on a similar footing as the question about what underlies gauge theory - this may be just an ill-posed question.

Of course the hope of most people is that there is a) some underlying theory whose vacuum states are given by the big blob, and b) on top of that there would be some dynamical mechanism that would weigh differently or select certain vacua. But there is no reason for a) and b).

I personaly like the idea as explained above, in that the big blob is like an abstract topological manifold M and any local quantum theory, one writes down corresponds to choosing local coordinates on M. The choice of origin of these coordinates corresponds to the choice of background around which one expands perturbatively. This does not at all mean that the fundamental object, M, would be meaningless and arbitrary, it just cannot be globally be described by local QFT. The fundamental theory, if it exists, would be some coordinate-free and thus some kind of topological theory without any local degrees of freedom.

This ties together with what I said before: there are no more elementary local degrees of freedom than we already know. Going up in energy does not reveal any new stuff. Still there exists a fundamental theory, and choosing a vacuum state produces an infinite amount of local degrees of freedom by expanding around it. This abstract underlying theory may or may not have any non-trivial dynamics.


This abstract pre-geometric theory is, I guess, similar in spirit to what the LQG people aim for. So I don't see here a fundamental disagreement.

 

[tom.stoer]

The differenc between string and gauge theory seems to be that strings allow one to solve for (SUSY/SUGRA) gauge theories as low-energy theories, so string theory somehow unifies gauge theories. Gauge theory w/o string theory is a collection of different theories only, the relation between them is construction not solution. Another difference seems to be that different (sectors of) string theories seem to be related by dualities i.e. some dynamic principles, whereas different gauge theories are related by copying the construction principles only. Going from SU(M) to SU(N) does not involve any physical principle.

Aiming for a fundamental topological or algebraic theory seems to be reasonable. But that means there are two tasks: identify the pre-geometric setting and find a principle which breaks it up into several patches and which induces or generates local degrees of freedom.

Again regarding the most promising research direction: what is your advice?

 

[suprised]

..., whereas different gauge theories are related by copying the construction principles only. Going from SU(M) to SU(N) does not involve any physical principle.

Well there are non-perturbative dualities that relate different gauge groups to each other. For example in N=2 Susy gauge theory, at large VEVS the theory looks like a pure SU(2) gauge theory, say, but at small VEVs it looks like a U(1) gauge theory with extra matter fields. Another example are Seiberg dualities for N=1 Susy Gauge theories, which relate theories with SU(n) and SU(m) and different matter content to each other. These theories, though looking "completely different" perturbatively, become equivalent in the low energy limit. That's very analogous to what happens to the higher-dimensional string theories.

Aiming for a fundamental topological or algebraic theory seems to be reasonable. But that means there are two tasks: identify the pre-geometric setting and find a principle which breaks it up into several patches and which induces or generates local degrees of freedom.

Indeed, but this is the hard part... bullgarbageting how what things should be like is easy. But actually doing it is infinitely much harder. And often one finds, by doing actual computations, that things turn out quite differently than expected. So there is not much content in bullgarbageting, unfortunately!

So that's why I don't know what to comment eg on Fra's remarks... much of it sounds quite reasonable, but putting flesh to it and make it concretely work, is 99.999999% of the problem and that's why 99.999999% of such generic ideas don't lead to anywhere, unfortunately.

Most promising for what precisely - uncovering the "underlying structure" of string theory? I don't have any concrete idea, nor do I know anybody who would. This seems a bit to hard a question to attack directly. So most ppl look for simpler toy problems where they hope to learn something about the inner workings of the theory. Most of this is quite technical work which doesn't tell much to non-insiders.

 

[tom.stoer]

Yes, that exactly my question: What is the most promising research direction in order to identify the unique, underlying, pre-geomeric structure of string theory and to identify the fundamental principle that explains how string- / M-geometry and their degrees of freedom emerge from it?

 

[Fra]

Indeed, but this is the hard part... bullgarbageting how what things should be like is easy. But actually doing it is infinitely much harder. And often one finds, by doing actual computations, that things turn out quite differently than expected. So there is not much content in bullgarbageting, unfortunately!

So that's why I don't know what to comment eg on Fra's remarks... much of it sounds quite reasonable, but putting flesh to it and make it concretely work, is 99.999999% of the problem and that's why 99.999999% of such generic ideas don't lead to anywhere, unfortunately.

For the record I fully agree with this and I certainly have no illusions that any of the things I suggests is easy. If it was easy, I would have done it already but I haven't. I certainly have not solve the problems! The way of reasoning towards solutions and problem formulations I suggests indeed also holds it's own hard problems, some of which are similar to those in ST. That is the one reason why I partly defended and sympathise with some of it's issues.

But I just think that just because it's so extremely complex, and that the journey from idea to concrete model is long, it's of even more importance so make sure we are working the the right direction, and it's true that we can not even for sure know that, but at minimum we should keep questioning our direction; it COULD save us lenghty detours. I've felt that this has sometimes been missing. In particular when experimental feedback is sparse, the science of model building becomes more important. When experimental feedback is ample model generation is not so important as it's quick to shoot down the wrong ones.

It becomes harder and harder to falsify theories, and that's why that framework whereby the candidates for falsification are important. We can't afford to spend time on carelessly built theories, because the lost investments if we are wrong are higher. This is another reason why I'm focusing more on a model building that is constructed as a rational learning or inference system. Here the "evolution" of the theory itself becomes a key point! A theory is no longer just a candidate that's either wrong and shot dead, or corroborated. It's something more, becase interesting things happen in particular when the theory is what we used to call "wrong". This however borderlines to the foundations of the scientific method, and also adaptive learning models.

There are similarities here also with string theory, as I see it. But probably more due to coincidence since the type of reasoning I advocate was not ever part of ST constructing principles, it's mostly similar to reflections that comes also from speculations towards solutions to some of the ST problems.

My original point in this thread (way back) was that I think it's superficial to dismiss ST just on the argument that it has no simple clean static timeless theory we can shoot down. Somehow it's noy what I seek either to be honest. I rather seek to understand the evolution of theories in the sense I've already mentioned, which by the way is one-2-on with the evolution of observers and particle properties.

Here it seems Tom has a slighly different critique.

But of course this is hard stuff. This is why trying to think in new terms may not be so bad after all.

/Fredrik

 

[marcus]

...This abstract pre-geometric theory is, I guess, similar in spirit to what the LQG people aim for. So I don't see here a fundamental disagreement.

Yes, that exactly my question: What is the most promising research direction in order to identify the unique, underlying, pre-geometric structure of string theory and to identify the fundamental principle that explains how string- / M-geometry and their degrees of freedom emerge from it?

Thanks, both. These observations go to the heart of the matter.

 

[tom.stoer]

your welcome :-)

it took us 255 posts to ask such a simple question, so I guess another 255 posts will suffice to derive 42 (or perhaps 10, 11,24 or 26)

 

[marcus]

your welcome :-)

it took us 255 posts to ask such a simple question,..

but many of those were interesting and enlightening posts, sometimes exceptionally so.

If as Surprised just said, he sees string/M and LQG having similar aims---they would not need to be precisely the same, for trading ideas to be productive---then we could try to learn something by comparison.

Maybe spin-networks (which are graphs labeled by group-reps) have something to suggest about the formulation of M-theory. A possibility even if seemingly remote.

Both your comments mentioned "abstract pre-geometry" as an important goal.

What would be a "post-geometry"?

Presumably to get a "post-geometry" one would throw away the continuum (the smooth manifold representing space or spacetime) and just consider the finite information which one can have.

[Information about what? ... the Umwelt? ...the space and matter relationships?...the experimenter's Experiment?...I'm sorry for the vagueness. The "what" is not mathematically represented, only the information about it.]

This is what I see happening in the two current papers that epitomize LQG and it's application to cosmology LQC: 1004.1780 and 1003.3483

Perhaps the idea is that at a very microscopic level we cannot tell if the world is smooth or not smooth. Does it even makes sense to represent it mathmatically as a set with some axiomatic structure? All we have, if we are lucky, is information from some measurements. The networks of LQG---the labeled graphs---represent that batch of information. So the approach as I see it could be called "post-geometry".

But I guess you could also think of it as an "atomic" pre-geometry. The nodes of the network are "chunks of volume" and the links of the network represent adjacency and the "glue of area" joining the chunks. Then if matter is to be added, fermions become labels on the chunks and Y-M fields are flux-labels through the glue-joints. Please don't take this concrete picture seriously . Maybe it helps sometimes to have two contradictory ways to view something, so I offer you the tension between seeing LQG as "pre-geometry" and as "post-geometry". Also since I can't claim expertise I urge anyone interested to read the March and April papers 1003.3483 and 1004.1780.

Conceivably glancing over at what the LQG are doing could help think of how the big M-gap could be filled.

 

[atyy]

your welcome :-)

it took us 255 posts to ask such a simple question, so I guess another 255 posts will suffice to derive 42 (or perhaps 10, 11,24 or 26)

Yeah, it's obvious string theory gets the wrong answer!

 

[tom.stoer]

No, it's correct.

42 = 2*24 - (10-4)

So you take twice the Leech lattice and subtract the number of compactified dimensions; it fits perfectly.

 

[tom.stoer]

It is interesting to compare LQG and ST from that perspective. Afaik Penrose already guessed spin networks w/o any indication from QG decades ago. And I don't know if the LQG guys had spin networks in mind when they started to identify the discrete structure underlying the loops / cylinder functions.

It is interesting how we construct our theories. First we try to write down an action with a huge symmetry - the larger the better. Then we work for decades to reduce these symmetries and identify the physical degrees of freedom. Crazy! There should be a shortcut from physical phenomena directly to physical degrees of freedom (I am not talking about global symmetries like flavour which are "physical"; I am talking about gauge symmetries, conformal and diffeomorphism invariance etc.).

Therefore a topological theory or an algebraic structure like spin foams is desirable for string theory. If local symmetries are an unphysical intermediate step we should try to find a different approach.

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)
Wittgenstein​

 

[atyy]

No, it's correct.

42 = 2*24 - (10-4)

So you take twice the Leech lattice and subtract the number of compactified dimensions; it fits perfectly.

OK so LQG is dead

 

[Fra]

There should be a shortcut from physical phenomena directly to physical degrees of freedom

Not sure if this was part of your joke but this sounds like you are putting up a quest for a general understanding of the process wherby an observer, goes from observations to establishing a symmetry of his observations? And how the inferred symmetries kept by the observer evolve as new observations are made?

If so, I share that quest with you.

/Fredrik

 

[tom.stoer]

No, the idea to avoid unphysical symmetries was not part of the joke.

My observation is that gauge symmetries are unphysical symmetries; they introduce unphysical degrees of freedom which have to be reduced to the physical one by gauge fixing. Gauge symmetries are used to guess Larangians respecting certain physical symmetries as it is easier to guess one Lagrangian from which everything can be derived instead of guessing the Hamiltonian plus all other symmetry generators (e.g. the full Poincare algebra) with the correct interaction terms. If you have ever seen the gauge fixed QCD Hamiltonian you will understand why we cannot guess something like that.

The question is if this process "Lagrangian with huge unphysical symmetry => gauge fixing => physical degrees of freedom" which in LQG reduces the theory to a discrete structure hides some physical aspects (which we do not know) or if the whole process is somehow "physical" (even if we do not understand why).

 

[Fra]

The question is if this process "Lagrangian with huge unphysical symmetry => gauge fixing => physical degrees of freedom" which in LQG reduces the theory to a discrete structure hides some physical aspects (which we do not know) or if the whole process is somehow "physical" (even if we do not understand why).

I think this is a good question and I for one thinks there is more to understand here.

I expect that due to our different views on structural realism I have a different view of symmetry than you. The nature of symmetries in this sense, and what is physical and what's not, is even closely related to what elementso the theory that should correspond to observables in a measurement theory.

About your statement that gauge symmetry is non-physical, I understand what you mean but there is also another way of seeing it, where it's not so easy to tell if it's physical or not. I more think of gauge symmetries and transient symmetries in that sense that a completely unbroken symmetry is trivial(non-physical), and if represented will decay as it's a waste of complexity due to it's redundancy. But I'm not sure I would say that this means that they are unphysical because there is a physical reason (historical reason) why the originally broken symmetry, was restored, and then become trivial, and dissappeared from the representation.

I think these are also hard problems but these are things I've been thinking about and I'm confident that there are a lot of things in this "process" that is of physical relevance.

If you consider a totally unboken symmetry, no observer would ever be able to distinguish it, since inferring and establishing the symmetry to some degree of confidence can by understood from collecting data from cases where the symmetry is broken. Somehow the broken symmetry cases is what justifies the notion of the symmetry, but only transiently. This is what may first seem like a paradox; as much as the discussion of what's physical in GR. This is also similary to the discussion of observer invariance; and how observer invariance is observed. I see the symmetry discussion as closely parallell.

/Fredrik

 

[Fra]

Addition: Where I FULLY agree is that in some mathematical attempts to construct the theories, THEN we introduce what I would call "mathematical redundancies" that are clearly unphysical, and here I agree with you.

I just went to the next step to suggest that even beyond these "mathematical" and physically empty complexions of the system description, I still see physical process behind evolving symmetries. Ie where a symmetry is emergent, and later decayed. They plane I understand this on is on the pure inference and datacompression level where you consider economy of representation. Here one can imagine a stream of observations, that once enough data is acquired emerges with a symmetry. But if this symmetry remains unchallanged, then the value of wasting memory on this becomes less, so the symmetry can be recompressed into a more efficient structure (because it is not challanged). At some point the symmetry just becomes part of the background of the observer and takes up no memory. So the physical representation of the explicit symmetry is ur survival value only when it's not abundant in the environment. That's how I see it conceptually but it's still apparentely extremely difficult ti implement this. It's part of what I hope to do, but it's not easy.

/Fredrik

 

[tom.stoer]

Just a clarificaton: I do not talk about broken symmetries.

Another remark: gauge symmetries are a powerful principle as they allow one to construct renormalizable field theories and to derive conserved quantities. So as a tool they useful, but they are not "directly realized in nature".

SU(3)_Flavor is more or less observed directly.

SU(3)_Color is identified rather indirectly, via the fact that there are three quarks in a proton. So it's not totally unphysical. But the SU(3) Lagrangian contains unphysical gluons which have to be reduced to the physical subspace. But in the physical subspace there is no SU(3)_Color symmetry left.

Think about a two-particle system where the interaction depends only on V(x-y). That means that the system is invariant w.r.t. translations as x-y is an invariant. The "physical subspace" in QM is the sector of the Hilbert space with vanishing total momentum P, i.e. P|phys> = 0 (this is not enforced by the theory by used in practical calculations). No in this subspace there is no translation invariance anymore; it has been eliminated by setting P|phys> = 0. Something like that happens in gauge theories as well; the fully gauge fixed theory with physical degrees of freedom does not contain any gauge symmetry.

In LQG its rather similar (even so not every body agrees on the implementation of the constraints as they are on-shell instead of off-shell). Both the gauge symmetry (local Lorentz invariance) and diffeomorphism invariance vanish in the physical subspace, the space of spin networks.

But unfortunately it is by no means clear how to derive the theory w/o going through all the gauge fixing issues. Simply writing down an SF model and claiming that it is QG doesn not help. One has to show how it followes from a quantization + constraint procedure.

In LQG there is a second approach how to derive the SF models. One starts with a topological theory (w/o any physical degrees of freedom) and introduces a term which breaks the huge invariance and in parallel generates physical degrees of freedom = which increases the number of physical polarizations of the gravitational field from 0 to 2.

Now let's come back to strings

What would that mean in the context of string theory? One would have to identify a topological theory = a theory w/o physical degrees of freedom; in a second step one would have to introduce terms which break these symmetries and at the same time generate physical excitations. Because one starts with a topological theory one has a good chance to define it globally (even so one would not succeed in identifying discrete structures immediately as a detaour via smooth manifolds is still used; but this manifold need not be our spacetime, it could be some "dual" entity as well; so discrete structures could emerge from a dual structure; see for example the Fourier expansion on a smooth circle).

Has anybody thought about that possibility? Are topological strings a good starting point?

 

[Fra]

Ok, I guess you ask much more specific questions defined the context of some of the current programs. I have no good comments on that level, as I find some of these questions to be somewhat open wires or patches partially floating in the current effective frameworks. My own strategy is to restructure from much more basic levels and build my understanding from there; the connection to the floating patches are yet remote for me.

/Fredrik

 

[tom.stoer]

Of course this question goes to the string theory experts.

 

[suprised]

Just a clarificaton: I do not talk about broken symmetries.

But that's what I had in mind... ANY kind of background would correspond to a (partial) breaking of whatever symmetry the underlying theory has, and the physical excitations would be like Goldstone modes for that background. These ideas are of course not new. Already in the early days ppl were considering eg scattering amplitudes at infinite energy, where the vertex operator algebra simplifies, and tried to uncover "fundamental" symmetries this way. Certainly these attempts were naive but it the spirit was OK.

So I think the relevant concept would be symmetry breaking; gauge fixing, BRST etc is not a physical principle, it has to do with the formulation of the theory.

Has anybody thought about that possibility? Are topological strings a good starting point?

There are several notions of topological strings. What one usually means by that is a toy model for superstrings and this is not what is meant here. There are other topological theories like Chern Simons, BF etc, and this is what I had in mind. Many things have been tried, also in the context of string field theory. But AFAIK one never could make the big step between writing down some simple topological action, and then deriving something non-trivial from it. Many ppl feel that such attempts are too naive.

 

[tom.stoer]

My remark regarding "not talking about broken symmetries" was in the context of "gauge symmetries are unphysical". I did not consider symmetry breaking there and I just wanted to clarify this in my discussion with Fra.

Of course you are right in the other context of deriving a dynamical theory from a topological setting like BF theory. I know gravity as constraint BF theory from Plebanski and LQG/SF. Yes, this is somehow a breaking of the underlying symmetry, but rather different from standard symmetry breaking a la Goldstone and Higgs as it generates local degrees of freedom, something which the Higgs does not! The Higgs simply transforms an already existing scalar degree of freedom into a new polarization state = a vector degree of freedom.

BF theory seemed to me rather artificial. One starts with a topological action - which is nice - and then constrains it in order to generate gravity. How can this step be motivated? I mean, why should one consider this to be physical if one did not knew that gravity should emerge? Is there a deeper principle behind it?

Regarding gauge fixing, BRST etc. we agree.

 

[MTd2]

It's work in progress by Witten.

He anounced that he will publish the ideas of his thought on citation 14 of his new paper:

http://arxiv.org/abs/1009.6032

 

[tom.stoer]

http://arxiv.org/abs/1009.6032
A New Look At The Path Integral Of Quantum Mechanics
Edward Witten
(Submitted on 30 Sep 2010)
Abstract: The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles in the path integral of this theory can be derived from N=4 super Yang-Mills theory in four dimensions. Hence, under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N=4 path integral in four dimensions.

therein

[14] E. Witten, “Fivebranes and Knots, I,” to appear.

... and show exactly how a quantum path integral in N = 4 super Yang-Mills theory on a four-manifold with boundary can reproduce the Chern-Simons path integral on the boundary, with a certain integration cycle. This has an application which will be described elsewhere [14]. The application involves a new way to understand the link between BPS states of branes and Khovanov homology of knots

I am sorry, but can anybody explain to me how this could guide us towards a more fundamental understanding of what string theory really is? Isn't this "yet another reformulataion"?

 

[MTd2]

I don't think so. This paper belongs to the same area and line of research of his Fields Prize.

 

[qsa]

Perhaps the idea is that at a very microscopic level we cannot tell if the world is smooth or not smooth. Does it even makes sense to represent it mathmatically as a set with some axiomatic structure? All we have, if we are lucky, is information from some measurements. .

This is the best statement I have read on PF. while the status of virtual particle as something between mathematical and real I can really understand. But GR statement that space-time is curved bugles my mind. Although, it is easy to see how it is a good modeling scheme just like virtual particles, but it is much less satisfying. I think statistical mechanics is the way to go.

 

[mitchell porter]

I don't know what else Witten's paper will lead to, but I believe it is indirectly relevant to quantizing M-theory. In fact, the philosophy is that M-theory is somehow "inherently quantum" - it has a classical limit, but the theory itself is not to be obtained by starting with that limit and "quantizing" it according to known procedures.

I have become aware of two specific technical issues. One is that the worldvolume theory of the M5-brane is "non-Lagrangian". The "geometric Langlands program" is somehow relevant here. The other is that there is no fundamental dilaton field in M-theory, so you can't construct a perturbative expansion as one does in string theory, where the dilaton field strength is the expansion parameter. arXiv:hep-th/0601141 talks about how this looks from the M-brane perspective.

I think these investigations by Witten into new perspectives on quantization pertain to these problems. Note that in the first part of this paper, he identifies an ordinary quantum-mechanical system with an "A-model" construction from topological string theory. If you turn that around, he's starting from within string theory and getting a quantum theory. Also, Chern-Simons fields show up in M-brane worldvolumes, so the second part may be relevant too.

 

[MTd2]

What is the meaning of something being non-lagrangian?

 

[suprised]

Not all QFT's have a lagrangrian description, in particular, strongly coupled ones, which cannot be represented in this way.

 

[MTd2]

Oh, that's quite a new thing for me! Well, but there's a hamiltonian description, right?

 

[suprised]

Not really. One needs to make sense of what one writes down, at the quantum level. Usually one needs to have a theory with some small parameter, like a coupling constant, and writes the theory as a perturbative series around the free theory, with this parameter as expansion variable. In this way one can compute the quantum corrections to the operators in the lagrangian or hamiltonian in a systematic manner; this is the content of the renormalization procedure.

But as has been pointed out above, not all theories are of this kind, like the M5 brane or non-critical strings in 6d or interacting conformal theories. There is no small parameter to expand into, so there exists no perturbative description of such theories and thus, no Hamiltonian or Lagrangian one would know how to write down starting from the classical one; since there is no classical one to start with.

Sometimes this is not even necessary, for example 2d conformal field theories like the minimal models. The correlators of those theories can be determined purely from consistency conditions, and one never needs to (nor even could) write down a lagrangian for them.