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  What are the details around the origin of the string theory?

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It is well-known even among the lay public (thanks to popular books) that string theory first arose in the field of strong interactions where certain scattering amplitudes had properties that could be explained by assuming there were strings lurking around. Unfortunatelly, that's about as far as my knowledge reaches.

Can you explain in detail what kind of objects that show those peculiar stringy properties are and what precisely those properties are?

How did the old "string theory" explain those properties.

Are those explanations still relevant or have they been superseded by modern perspective gained from QCD (which hadn't been yet around at the Veneziano's time)?

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Marek
asked Aug 18, 2011 in General Physics by Marek (635 points) [ no revision ]
retagged Mar 27, 2014 by dimension10
My experimental thesis was using Regge poles to search and explain resonances seen :). Regge poles are still there. Their value as an organizing substructure was undermined when the eightfold way first showed the value of symmetries, and then of course the SU(2)xSU(3)xU(1) success as the standard model erased them from memory . I have always thought of all string incarnations as the multiple uses of the harmonic oscillator solutions, which are really the first symmetric function in a series expansion of any potential.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user anna v
@anna: The Regge theory is enjoying a remarkable comeback. It was unfairly maligned. People are now discovering that S-matrix theory is the best approach to perturbative supergravity, and the mysterious structure of QCD Regge poles is again active in AdS/QCD. Regge theory wasn't a fad.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Ron Maimon

3 Answers

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in the late 1960s, the strongly interacting particles were a jungle. Protons, neutrons, pions, kaons, lambda hyperons, other hyperons, additional resonances, and so on. It seemed like dozens of elementary particles that strongly interacted. There was no order. People thought that quantum field theory had to die.

However, they noticed regularities such as Regge trajectories. The minimal mass of a particle of spin $J$ went like $$ M^2 = aJ + b $$ i.e. the squared mass is a linear function of the spin. This relationship was confirmed phenomenologically for a couple of the particles. In the $M^2$-$J$ plane, you had these straight lines, the Regge trajectories.

Building on this and related insights, Veneziano "guessed" a nice formula for the scattering amplitudes of the $\pi+\pi \to \pi+\rho$ process, or something like that. It had four mesons and one of them was different. His first amplitude was the Euler beta function $$ M = \frac{\Gamma(u)\Gamma(v)}{\Gamma(u+v)}$$ where $\Gamma$ is the generalized factorial and $u,v$ are linear functions of the Mandelstam variables $s,t$ with fixed coefficients again. This amplitude agrees with the Regge trajectories because $\Gamma(x)$ has poles for all non-positive integers. These poles in the amplitude correspond to the exchange of particles in the $s,t$ channels. One may show that if we expand the amplitude to the residues, the exchanged particles' maximum spin is indeed a linear function of the squared mass, just like in the Regge trajectory.

So why are there infinitely many particles that may be exchanged? Susskind, Nielsen, Yoneya, and maybe others realized that there has to be "one particle" of a sort that may have any internal excitations - like the Hydrogen atom. Except that the simple spacing of the levels looked much easier than the Hydrogen atom - it was like harmonic oscillators. Infinitely many of them were still needed. They ultimately realized that if we postulate that the mesons are (open) strings, you reproduce the whole Veneziano formula because of an integral that may be used to define it.

One of the immediate properties that the "string concept" demystified was the "duality" in the language of the 1960s - currently called the "world sheet duality". The amplitude $M$ above us $u,v$-symmetric. But it can be expanded in terms of poles for various values of $u$; or various values of $v$. So it may be calculated as a sum of exchanges purely in the $s$-channel; or purely in the $t$-channel. You don't need to sum up diagrams with the $s$-channel or with the $t$-channel: one of them is enough!

This simple principle, one that Veneziano actually correctly guessed to be a guiding principle for his search of the meson amplitude, is easily explained by string theory. The diagram in which 2 open strings merge into 1 open string and then split may be interpreted as a thickened $s$-channel graph; or a thick $t$-channel graph. There's no qualitative difference between them, so they correspond to a single stringy integral for the amplitude. This is more general - one stringy diagram usually reduces to the sum of many field-theoretical Feynman diagrams in various limits. String theory automatically resums them.

Around 1970, many things worked for the strong interactions in the stringy language. Others didn't. String theory turned out to be too good - in particular, it was "too soft" at high energies (the amplitudes decrease exponentially with energies). QCD and quarks emerged. Around mid 1970s, 't Hooft wrote his famous paper on large $N$ gauge theory - in which some strings emerge, too. Only in 1997, these hints were made explicit by Maldacena who showed that string theory was the right description of a gauge theory (or many of them) at the QCD scale, after all: the relevant target space must however be higher-dimensional and be an anti de Sitter space. In AdS/CFT, much of the original strategies - e.g. the assumption that mesons are open strings of a sort - get revived and become quantitatively accurate. It just works.

Of course, meanwhile, around mid 1970s, it was also realized that string theory was primarily a quantum theory of gravity because the spin 2 massless modes inevitably exist and inevitably interact via general relativity at long distances. In the early and mid 1980s, it was realized that string theory included the right excitations and interactions to describe all particle species and all forces we know in Nature and nothing could have been undone about this insight later.

Today, we know that the original motivation of string theory wasn't really wrong: it was just trying to use non-minimal compactifications of string theory. Simpler vacua of string theory explain gravity in a quantum language long before they explain the strong interactions.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Luboš Motl
answered Aug 19, 2011 by Luboš Motl (10,278 points) [ no revision ]
+1, but a quibble--- I don't agree that "strings" by themselves demystify world-sheet duality, they just give it a clear picture. They explain duality if by "strings" you mean that there is only one open string diagram, but this is a duality assumption. Imagine scattering of physical rubber bands--- they can be exchanged in t-channel or s-channel, and you have to sum the two contributions, they are separate. New virtual rubber bands are produced at collisions at localized points, not by smoothly opening the topology like a string diagram. Duality says string aren't like rubber bands.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Ron Maimon
Very nice answer (which is why I accepted) but I'd like to understand how the spectrum is explained from the modern point of view. Obviously the old theory doesn't work (as you mention it contains graviton, etc.) but equally obviously there are some underlying strings present (since this is the only natural explanation of the trajectories). Ron hints at this in his comment about AdS/QCD as well. I'll ask this as another specific question though (unless one of you will tackle it directly in comments here).

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Marek
Dear Marek, string theory always contains gravitons when it's studied correctly and consistently, so the confusing massless spin-2 mode was always there and was always confusing for anyone who tried a strong interaction-like interpretations. In fact, the bosonic string theory also had a tachyon which is much worse. ;-) For a few years, there was a confusion about such things - whether you could move the spectrum, choose any spacetime dimension you wanted etc. so there was a lot of unjustified hope it would work. Within years, $D=26$ and tachyon+graviton's inevitable existence was settled.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Luboš Motl
Dear Ron, I don't think that your comment is right. Strings in string theory are "relativistic rubber bands" while normal rubber bands are made out of atoms that pick a special frame and obey a Lorentz-breaking world volume theory, but this is the only difference. Rubber bands, much like strings, would still respect the world sheet duality. Well, at least any rubber bands that could be continued to the Euclidean spacetime. In particular, you can't create a whole rubber band at a single point. Rubber bands are 1-dimensional so you may only create them 1 point/atom at a time, one after another.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
Ron, when you say that rubber bands could distinguish the s-channel and the t-channel, it seems that you are using the word "rubber band" but you are actually not treating them as rubber bands. Rubber bands, by definition, are one-dimensional objects. One-dimensional objects inevitably have 2-dimensional histories in spacetime - world sheets or "rubber sheets" - and these histories "geometrically" always work like in the string case, and this geometry is enough to see that no qualitative separation of s-channel and t-channel diagrams may exist.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Luboš: I am aware about the rest of the string history and the significance of the spin-2 mode. But this isn't the correct theory of interacting hadrons. The case is actually similar with the history of SU(2) interactions which were first proposed for strong interactions but there they couldn't work and were later revived in the weak case. Now, strings were revived as a theory of quantum gravity but (at least in the old formulation) they can't work as the effective hadronic theory one was looking for originally. My question is "what is that theory then?".

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Marek
Dear @Marek, well, not quite, as I have indicated, the right background of string theory is the correct theory of hadrons. We call it the "QCD dual". This isn't quite perfectly and accurately understood for ordinary real QCD but it is beautifully understood for a very similar theory, the N=4 gauge theory in d=4, which is exactly equivalent to type IIB string theory on AdS5 x S5. The equivalence is known as AdS/CFT. So strings can work as those things - this is what much of the last 15 years were all about. String theory is all of these things and much more.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
Just to be sure, non-SUSY QCD is ill-behaved from many viewpoints but there are many other gauge theories with as low as N=1 supersymmetry whose string theory dual is understood more or less rigorously, almost on par with the N=4 case. Various bases of the conifolds, Einstein spaces, etc., and one gets gauge theories with various kinds of chiral supermultiplets. So as I have tried to emphasize, but apparently unsuccessfully, the original motivation of string theory was proved correct as well, one just needed some extra work and understanding of subtleties of the right backgrounds.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Luboš: you're a funny guy :) Your point that string theory is a correct theory both for quantum gravity and hadronic physics has been communicated across well and I've actually understood for some years now. What you failed to understand though that I have no interest in terms such as "theory of everything" and am instead interested in the precise theory (precise model, particle content, initial conditions, whatever) that explain hadronic processes. So thanks that you've finally addressed this question directly ;)

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Marek
In other words, one should distinguish between the old string theory (which didn't work for hadronic interactions) and modern interpretation of string theory that includes M-theory, branes, landscape and whatnot. The modern view of course encompasses much much more than the original theory did but is also quite useless unless one specifies compactifications, etc. It would be nice if you spent less time on spreading string theory propaganda (which is actually not needed at all since I like strings a lot) and instead focused on the concrete physics :)

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Marek
@Lubos: I don't think you are right for what people think of as ordinary "rubber bands". The free action might resemble a string action, but a naive collection of point particles with delta-repulsive interaction will have generic self-intersection interaction wherever the world-sheet self intersects, so their interactions cannot be given by a local worldsheet theory (although the free propagation might). If you look at how string theory gets around that, its by worldsheet duality, that the interactions are all due to exchange of strings, and this is an additional assumption (Chew's bootstrap).

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
To expand a little--- in string theory, you use S-matrix asymptotic states as the objects which are exchanged between the strings (which for linear Regge trajectories turns out to be equivalent to summing over worldsheets), without asking for more fundamental things of which these things are built, and without allowing arbitrary interactions between the fundamental things to kick in at high energies. So it is automatically a theory of everything if it is a theory of anything. I think this was understood by the bootrstrap community to a certain extent even in the 1960s.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
Dear @Marek, you write: "I have no interest in terms such as 'theory of everything'". If you're not interested, why did you ask a question exactly about this question on Physics Stackexchange? Your comments about your being interested in a particular "model" shows that you still misunderstand the structure of string theory. String theory is not "many models". String theory is a single, unified, totally inseparable theory. You can't cherry-pick string theory. It's one set of equations that has a large landscape of solutions. All of them are valid, all of them show different phenomena.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
In other words, @Marek, the key comment is that string theory is a "theory of everything" - which I didn't really use: I said that it was both a theory of gravity as well as the strong force, and the strong force emerges from string theory in several different ways, either as a "part" of a full description of all forces, or - via AdS/CFT - as "just QCD" from an AdS background. This seems to be the very point of your question, at least the followup questions you added. So I can't understand why you're so hysterically trying to hide your head to the sand when I am telling you the answer.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
Dear @Ron, 1-dimensional objects almost never self-intersect in spacetime of higher dimension of 3+1, e.g. $D=26$ or $D=10$, so this is a measure zero problem and you may completely forget about it. An even more obvious "measure zero" situation that may be ignored is when all atoms of a rubber end are located at the same point - which, by the way, can't happen at all if the rubber bands are made out of atoms such as the real rubber bands. The bulk of the dynamics of a string or a rubber band - it's totally analogous in both cases - is given by the dynamics of 2-dimensional world sheets.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
Concerning your second comment, @Ron, once you adopt the assumption that the physical objects are made out of strings, the rest of the theory - including all the details about the ways how these things may interact - is completely determined by consistency - unitarity or, equivalently in the light-cone gauge, Lorentz symmetry. There is not a tiny bit of choice or freedom to "adjust" string theory. String theory is a single, totally rigid structure without any adjustable dimensionless parameters and it has a totally well-defined set of solutions. There's no way to "deform" string theory.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
What I want to say is that it is the opposite of the truth to suggest that string theory might be a theory of "anything". All previous theories in physics admitted some deformations or continuous parameters that were labeling different theories - but string theory doesn't. For example, interactions of rubber bands that would be nonlocal on the world sheet would also break spacetime locality and spacetime unitarity and spacetime Lorentz symmetry, and so on. Consistency prohibits all pathological mutations of the theory and string theory is totally determined by consistency.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Luboš: I think you misunderstood lot of what I said and I have misunderstood you as well. I am only a little allergic of your omnipresent strong support of string theory which often stops being to the point and rather sounds like ideology. I have no problem with accepting string theory as a ToE (that's my own worldview actually, at least tentative) and likewise I have no problem in accepting that hadronic physics can be explained by supergravity through duality. But I'd like to learn more about this concrete setup instead of hearing in every second comment how great string theory is...

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Marek
Besides +Marek criticisms, it seems to me that some reference to the discovery of Ramond string should be done when answering a question about "details around the origin" of String Theory. Spin 1/2 was there from the start, but somehow, perhaps due to its failure to match the baryons, or perhaps due to troublesome interpretations (as quark-gluon duality), they are not mentioned until the advent of the spacetime superstring.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user arivero
Dear @Marek, the statement that string theory is a single theory is not ideology: it is a key technical property of the theory. Even if you decided to call it ideology - be my guest - it is a totally crucial ideology to understand what the theory actually is and what it is not. So it's just too bad if someone cannot learn these crucial technical things without "allergies". Arivero, Ramond's string - and Neveu-Schwarz string - wasn't really an "origin of string theory". String theory had "origin" as bosonic string theory which has no fermions. All SUSY/fermioncs strings are "new".

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Lubos: The condition for quantum strings to intersect is not that the dimension is $\le 4$, even though this is the condition for classical strings, and this condition is used by Brandenburger/Vafa. Quantum point particles intersect generically in 3 dimensions, and are marginally intersecting in 4 (the same as $\lambda\phi^4$ running. The intersection dimension of the string will surely be very large. Whenever I try to calculate it, though, I get infinity because the box-counting is impossible when the field fluctuations run away at small distances.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
@Lubos: as for the other stuff, I can construct an example field theory with low energy "strings" but high energy crap for you, but I do not want to fill up the comments. I will do so as an answer or a question. I know this is possible because I tried to find string theory by following the propaganda, but it is impossible to derive the interactions without knowing that the only way strings interact is by exchanging strings, and not something else.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
Dear @Ron, Brandenberger-Vafa or string gas cosmology etc. isn't a paper about the existence and character of fundamental interactions in string theory; it is a paper about the "derived" impact of geometrical arrangement of strings on cosmology. Whether the strings are intersecting or not is irrelevant and the rules for the interactions of strings are independent of the spacetime dimension and they work in such a way that you may neglect the possibility of self-intersection as a measure-zero problem: the world sheet is always smooth around the interaction "point", even in $d=2$.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
Dear Ron, you write: "I can construct an example field theory with low energy 'strings' and high energy crap". Great. You may construct such a "theory". But I may easily prove why it is crap and not a consistent theory i.e. not string theory. You can't modify string theory at high energies or low energies without spoiling its consistency. Of course, you may produce lots of crap but crap isn't the same thing as a theory in physics. One may prove that string theory can't be added ad hoc point-like-particle-like interactions without spoiling its consistency.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
By the way, your "counting of the intersection dimension" in string theory is crap, too. There is absolutely no reason why such ad hoc concepts should be well-defined in a physical theory and they're not. Much more generally, the concept of "total spacetime dimension" is extremely subtle - the number of "Planckian" or "stringy" sized dimensions is always ambiguous and different dual descriptions generally yield different answers: ST isn't a fully local QFT, after all. Only large dimensions - much larger than the string/Planck scale - can be "unambiguously" counted.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Lubos: I agree with you about the properties of standard string theory completely, uniqueness yada yada. What I am trying to make you understand is that there are hidden bootstrap assumptions used in constructing the standard theory. I agree with you about dimension counting for strong coupling, it is totally wrong, but that's because of the bootstrap nature of the string. Naive dimension counting for getting intersections in nearly flat space works for crap-strings (rubber bands). The fractal dimension of the embedding might be nonsense for real strings, but that's not the point.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
Dear @Ron, it's very interesting. But could you please be a little bit specific what the "hidden [bootstrap] assumptions" are? It's hard to imagine anything real behind your words at this point. I was just innocently stating that the particular deformation of string interactions you proposed was inconsistent. As far as I can say, one can prove it without any assumptions that would have to remain "hidden". You: "The fractal dimension of the embedding might be nonsense for real strings, but that's not the point." - OK, but what is your point then? Fractal dimension depends on UV physics.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Luboš Motl
@Lubos: I wasn't proposing a "deformation" of strings, I was telling you that you are using bootstrap assumption that the string exchanges other strings and nothing else. This is not demanded by any consistency condition (except for being a correct holographic gravity theory), and there are models of stringlike objects in which it fails.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
@Lubos: here is a model physics.stackexchange.com/questions/13828/chentile-strings.

This post imported from StackExchange Physics at 2014-03-17 04:02 (UCT), posted by SE-user Ron Maimon
+ 4 like - 0 dislike

I liked this video, where Susskind explains how he and some friends discovered string theory in the context of meson scattering.

(This is just a very preliminary answer, the video is probably way below your level ... :-P, I will take it back as soon as it is superseded)

answered Aug 18, 2011 by Dilaton (5,240 points) [ revision history ]
You`re welcome :-))). He starts drawing a plot of the Regge Trajectories and in the course of the lecture nicely derives it from meson scattering, including the transformation to light cone coordinates step by step. I dont remember all of the details, will have to rewatch it when I busy myself more seriously with the whole string course of Lenny Susskind ...

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Dilaton
+ 3 like - 0 dislike

Well I believe the original clue was Regge trajectories. It was observed that if you plotted mass squared vs. angular momentum for strongly interacting resonances, they tended to follow straight lines. This could be explained as the spectrum of rotating strings connecting massless particles.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user user1631
answered Aug 18, 2011 by user1631 (60 points) [ no revision ]
This is what I've heard as well.

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user David Z
Interesting. What I heard about the origins was actually something to do with Veneziano and beta function. How does this relate?

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Marek
Okay, I think I can answer my own question. Since the spectrum lies on the Regge trajectories it means it can be interpreted as the poles of the beta function. I'd still want to have more details though (ideally a reference).

This post imported from StackExchange Physics at 2014-03-17 04:01 (UCT), posted by SE-user Marek

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