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What is a glueball ? January 4, 2009

Posted by dorigo in Blogroll, physics, science.
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This post is just a placeholder for a link and an invitation for you to join me and ask Marco Frasca to further his already enlightening discussion of glueballs, as I already did in the comments thread of his post.

The subject is indeed fascinating: gluonic matter. A condensate of bosons. Asymptotic states (particles) made of no fermions. Matter as we never experienced it.

Glueballs are (thought to be) bound states of gluons. The gluon, the carrier of strong interactions, is a massless boson, and it is charged with the attribute it mediates: colour. Because of the colour charge of gluons, these particles can interact with one another, giving rise to the fascinating properties of Quantum Chromodynamics, the asymptotic freedom properties of bound states of quarks, and the infrared slavery – the impossibility of obtaining free coloured objects (quarks or gluons). The non-abelian nature of the SU(3) group underlying quantum chromodynamics is a source of the difficulties of calculating the low-energy limit of the theory.

The self-interaction properties of gluons creates the possibility of a color-neutral state made of gluons only: glueballs. Glueball properties, however, cannot be computed with perturbation theory, and these remain very mysterious objects over thirty years after QCD was understood in its workings. Only with lattice calculations -you know, discretizing space and computing path integrals with finite sums- can the glueballs be understood. But Marco hints at methods that allow a deeper understanding: methods based on condensed matter physics. We are all ears!


1. Luboš Motl - January 4, 2009

I find this hype about glueballs bizarre and irrational. In my optics, “glueball” is a placeholder for the most uninteresting, structureless, anonymous, and uncalculable state one can get in a gauge theory. Whenever you encounter such dull “particles” in a description of gauge theory, you may call them glueballs.

They carry no nontrivial quantum numbers. So by a dimensional analysis, a theory with no dimensionless couplings like QCD should predict a width – decay rate – of these particles, and they should be of order the QCD scale, anyway. It’s enough for them to be allowed to decay, which they certainly can in a theory with quarks like the real world QCD.

So the mass is remotely comparable to the width and the very question whether it makes sense to talk about special particles is very controversial because we only talk about “particles” when their width is much smaller than the mass i.e. if the lifetime is long enough. Sure, the lifetime can get suppressed by discrete constants such as functions of the number of colors but for N=3, we don’t get much of it.

It is also wrong to say that they’re made purely of gluons. In the strongly coupled regime that is appropriate, they’re made of loops of any other physics that you find in your game, including contributions of quark-antiquark pairs. But even if they were made out purely of bosons, I see absolutely nothing to be excited about. Hydrogen is also made out of bosons – the Hydrogen atoms (or molecules). And what? A boson is obtained by taking a bound state of an even number of fermions, too.

You could say that gluons are different because they’re elementary particles. But the whole separation of particles to elementary and composite ones depends on the effective description, anyway. Particles that look elementary or weakly coupled in one description or limit become composite or solitons in another limit. Gluons in perturbative string theory, to take an example, are states of a single string but you can view the string as a bound state of infinitely many “string bits” which are partly fermions. There is nothing religious about the difference between bosons and fermions much like there is nothing religious about the difference between particles with an integer or non-integer electric charge. This difference is just a technicality. Obviously, any theory capable to deal with the real world, or anything remotely similar to it, must equally easily deal with both bosons and fermions.

Also, I find strange Marco’s last statement:

“Of course quantum gravity may be more rewarding but, what if one has a tool to solve any differential equation in physics in a strong coupling regime? Should you call this a scientific revolution?”

Whether or not things are called a revolution, the fact that one should consider effective theories at long enough distances is not quite due to “condensed matter physicists”. It is primarily due to quantum field theorists such as Ken Wilson, so the attribution of this stuff to condensed matter physics is just unfair.

Moreover, Marco exactly hit the big issue: the *really powerful* method to solve strongly coupled theories is nothing else than quantum gravity (like in AdS/CFT). So the answer to the question whether quantum gravity is more fundamental than a method to solve strongly coupled gauge theory (for a person interested in QCD only) is that they’re equally fundamental because they’re the very same thing.

However, string theory clearly offers much more than just some methods to solve some of these dirty things in strongly coupled gauge theory: they are concerned with the behavior of any conceivable quantum system and the basic laws that govern them. That’s why string theory is much more profound than any individual result about the strongly coupled theories in isolation.

Whether or not the word “scientific revolution” is appropriate, string theory is undoubtedly deserving the label much more than any of the other collections of insights that Marco or anyone else has mentioned. By orders of magnitude. There’s just way too much of a religious confusion about mundane terms in physics – like the difference between the bosons and fermions – that is driving most of the non-stringy hype in theoretical physics. All these things are old, well-known stuff.

2. dorigo - January 4, 2009

Hi Lubos,

your comment is very valuable, as always when you are not in the “piss everybody” mood. I am unfit to argue against what you say, despite my skin feeling that we will learn a lot from low-energy QCD one day, and that gluon condensates might hide surprises to us. I hope Marco can contribute here by answering where he is called in question.


3. mfrasca - January 4, 2009

Hi Lubos,

As always I appreciate to hear from you and this gives me a chance to clarify some essential points.

It is blatant that your view is strongly biased by the beauty of string theory but here on Earth we have some more mundane problems. The most important of these problems is to understand the light unflavored meson spectrum that to define a mess is not so far from truth. This problem involved also ‘t Hooft in a recent publication with Luciano Maiani and others where they claim that tetraquarks clarify all the matter. And they may be wrong. The stake is very high here and we have no way so far to understand reliably physics at strong coupling other than lattice computations and also here one can have reasonable doubts.

An example is general relativity. We are not able to prove any effect in strong gravitational fields. Some of these effects lie at the border with a quantum treatment and so, some understanding here will be helpful for both sides. E.g. I think to BKL conjecture that has obtained confirmation only through quite recent numerical computations.

Other problems can be found in condensed matter physics, quantum optics and and so on. I think the readers of this blog can add their preferred ones. Benefits for knowing a general approach to solve differential equations with a large parameter will pervade all physics at any level. Also string theory.

Let me turn now to Maldacena conjecture or AdS/CFT correspondence. Presently this approach is useless for QCD. Rather it seems that is QCD that could prove Maldacena’s right. I would like to remember that Witten claimed some years ago that Maldacena’s approach is the better way in physics to solve the mass gap problem. Current computations through AdS/CFT can be only pursued given the first value in the spectrum that is generally taken from lattice computations that are not granted to be fully correct. So, presently, AdS/CFT computes the spectrum given the mass gap!

My conclusion is that presently we have gained nothing from string theory, even if I can appreciate its beauty and perfection, to solve our more mundane problems. History of physics taught us that one cannot know where a breakthrough can come from and one should take both eyes and ears widely opened. An approach that assumes a priori that this is bad and that is good is simply doomed.



4. Luboš Motl - January 4, 2009

Dear (Tommaso and) Marco,

thanks for your comment even though it is questionable whether I should actually thank: I am not “biased” in any way. What I write is nothing else than the objective truth. 😉

Let me say that the popular, often repeated comment that “you face mundane problems” to distinguish QCD from string theory is both manipulative and untrue. QCD and string theory are two theories with no direct economical applications for the society, so any appraisal of their importance must be decided by their theoretical merit.

In fact, important (slightly modified) major parts of these two theories are equivalent so they’re equally “mundane” – which is an adjective that you clearly use as a positive one but I don’t. So how do we rationally judge the relative theoretical merit of ideas and research directions?

For example, I have no idea why you think that “tetraquarks” clarify “everything”. I find it obvious that tetraquarks are just other types of particles in QCD, about the 85th objects in QCD if sorted according to their importance, and QCD is just one segment of our description of the real world.

What on Earth do you mean by everything? You seem to randomly pick one of millions of technicalities and say that it is “everything”. It seems so ludicrous that I am not getting whether you are being serious or you just want to provoke me with this stuff. Isn’t it obvious that the claim that “tetraquarks are everything” is equally ludicrous as the statement that “physics of the gold atoms is everything”? What’s the difference? A tetraquark is just another bound state much like a new element.

The most important real, color-neutral particles are mesons and baryons which have roughly 2-3 “main” quarks or antiquarks. There are infinitely many excited states (and poles in the scattering amplitudes) of various types (and masses and widths) and a sensible person can’t ever say that the 85th of them according to some natural ordering is “fundamental” or “everything” or any of the crazy overhyped words you used.

Moreover, when you talk about strongly coupled gauge theories, string theory is not really just “a” method to approach the problem. The actual physics – what people can observe and measure – *is* a sort of string theory, so any correct approach is just another method to study string theory in a certain background.

Whoever thinks that physics in that regime has nothing to do with string theory is simply wrong about the broad sketches of physics. It is not a matter of opinions. There are “non-stringy” methods to study these issues but nevertheless, these methods still have to agree with certain general conclusions that can be derived from string theory because the stringy description is correct, at least with certain assumptions and limitations.

Also, I am not quite getting why you consider the BKL singularity to be that important. Why do you think that the questions about the behavior in the BKL singularity regime are more important than e.g. solving the carbon atom (or some molecules with carbon) in nonrelativistic quantum mechanics? The carbon atom and organic molecules have at least a deep importance for life. Whether the BKL singularity is relevant for anything in the real world is a highly uncertain question. It’s just another homework problem in GR, a homework exercise 13.5 in a textbook of GR.

You say that the readers may add their own problems – that are supposed to be automatically considered fundamental just because they add them. Interesting. Well, the reason why scientist should be able to objectively judge the importance and fundamental character of various things is exactly that he shouldn’t be adding random stuff just because it is convenient for his life if others consider it fundamental.

It should always be possible – and expected by the natural pressures of the environment – for scientists to move from less important problems to more important problems. A problem doesn’t become objectively important just because someone – who never wants to switch – has worked on it.

Also, I have no doubt either about the existence of the mass gap or the validity of AdS/CFT. In principle, I can talk about their possible invalidity much like I can talk about the extraterrestrial aliens controlling all of us together with Elvis Presley from the Moon. But beyond some point, I don’t particularly enjoy such discussions, especially if some people around consider themselves smart by talking about these extremely unlikely possibilities.

While we could perhaps academically say that the mass gap hasn’t been rigorously proven, the QCD mass gap is effectively a sure thing, and assuming it is effectively equivalent to assuming that 2+2=4. I am simply not too interested in lines of reasoning that are based on (sets of) assumptions that are excessively unlikely, especially if the conclusions about the unlikely world would fail to be more spectacular than the conclusions built on realistic assumptions. There are no high-quality arguments suggesting that the mass gap doesn’t exist, so why should scientist spend much time with that?

The whole purpose of science is to be closing the wrong eyes and keep the correct eyes open only – i.e. to falsify wrong theories. If you find this step cruel or undemocratic or impolite or whatever, you shouldn’t be doing science because science is cruel in this sense, by its very definition. And I don’t believe that the people who like to repeat this postmodern stuff about all questions being forever open are open-minded at the end. Virtually all of them end up with believing so many wrong dogmas that their conclusions become worthless. One always has to believe something – the question is who is right and science is a rather specific method to find the right answers after some effort.

One should be open-minded but the degree to which one is ready to believe a certain assumption should depend on the probability that it is correct as derived from the best evidence science can offer at this point. Whoever is open-minded according to different (“more egalitarian”) ratios than those that follow from scientific arguments is approaching the world irrationally (and unfairly, according to the scientific fairness).

So because the probability that mass gap exists in QCD exceeds 99.9999%, any person who assumes that it doesn’t exist 50% of the time is twisting or skewing the scientific evidence by a factor of one million. One can occasionally do such things but whoever is doing these things systematically is simply not doing science in any sense I can recognize.

Best wishes

dorigo - January 4, 2009

Hey Lubos, I question your point that both QCD and ST are useless to society. It is of course the case of ST, but knowledge of QCD is crucial for us to build efficient proton irradiation facilities, just to give an example. Scattering allows to treat multiple patients with the same beam, for instance. And the creation of isotopes is another application where QCD plays a role, albeit a marginal one. In general, however, knowledge of low-energy QCD may open up avenues for applications we do not dream of right now, but certainly are 10^15 times more likely to be practical than some advances in ST.


5. mfrasca - January 4, 2009

Hi Lubos,

You are completely off the track. I am sorry for this. I do not work on string theory and my problems cannot be solved by this theory in any way. You did not answered to my questions and you missed most of what I have said.

I said that ‘t Hooft and Maiani thinks that tetraquarks explain the light unflavored meson spectrum and they may be wrong. I cited them because they are well known physicists and they have chosen this problem because they consider it truly challenging.

I cited BKL as an example, but there are many many physical problems where only computers can help. Of course, blog’s readers can add lot more.

The existence of a mass gap is not in question here. I just proved to you that string theory cannot be of any help and not even the full Lagrangian of the standard model can be. So, claiming as you did that AdS/CFT is helpful for QCD is wishful thinking for the moment.

Finally, I accepted the scientific criteria and method since the start and I am exposed with my ideas that have been published on almost 60 articles in archival journals. Otherwise I would have left academia.

Finally, a simple question. If I had a method to do perturbation theory with a parameter \lambda\rightarrow\infty for any differential equation, dual to standard weak perturbations, would it be a scientific revolution?



6. Luboš Motl - January 5, 2009

Dear Tommaso,

I don’t believe that you actually believe what you write because it’s such a flagrant nonsense…

Saying that some detailed questions about tetraquark spectrum is useful for “proton irradiation facitilies” is only a method to confuse taxpayers with IQ below 60. You can’t be serious.

Open papers on scholar.google.com that mention “proton irradiation facility”. There are 204 of them now:


There are 406,000 papers that mention QCD. Now, you claim that QCD is useful for protons irradiation facilities. This conjecture of yours predicts that a significant fraction of the proton irradiation facility papers mention QCD. But in reality, you will find exactly one (2008) paper with both terms:


Your hypothesis is falsified in a very brutal way. QCD has nothing to do with irradiation facilities in practice. But people in QCD and elsewhere have gotten so used to lying to the taxpayer in this flagrant way that they don’t even realize that they’re lying: they began to lie to themselves.

Dear Marco,

I am not saying that everyone must work on string theory. Such a statement would be meaningless because one cannot invariantly divide science into what is string theory and what is not – that’s the whole point of a theory of everything. I am saying that your work on *QCD* is wrong if you disagree with the conclusion that a strongly coupled gauge theory is equivalent to a theory of strings.

Strongly coupled gauge theory with many colors simply is equivalent to weakly coupled string theory and any QCD expert who is not wrong – whether he likes to talk about computers, tetraquarks, glueballs, or chiral perturbation theory – must agree with this basic insight, otherwise he is misled about very basic features of his own field.

There is no separation between these sectors of QCD, do you get it? You can’t be just “non-stringy” by denying AdS/CFT: instead, you are simply wrong about the very field that you claim to be yours if you do it.

For some problems, computers are helpful, for others, they’re not. Neither answer means that the problems are more fundamental or less fundamental. If you think otherwise, you’re crazy. In fact, problems that are “really” understood must be understood without computers.

I don’t quite understand your final question, but if I give the question the most specific meaning I can imagine, the answer is surely No. In fact, what you write is similar to “a perturbative window to non-perturbative physics” by Dijkgraaf and Vafa


Perturbative methods can be used to completely reconstruct non-perturbative physics for huge – and in some sense “complete” – classes of models. But Dijkgraaf-Vafa was technically just a minirevolution, not a revolution. At any rate, it doesn’t seem like you have found that one.

Again, your precise project is vaguely described, so I must guess what it could exactly mean. If you claim that you could find the weakly coupled dual description for the strong coupling limit of any theory – one would have to define what is any theory or any differential equation (one??) – that would be an interesting result but not a revolution either.

The scientific revolutions occur when some completely new possibilities are opened, not when one solves a particular mathematical problem whose solution has been pretty much known before. So discovering the holography in QG – and the gauge-theory/gravity equivalence – was close to a scientific revolution. But solving a class of models is just another paper about holography. Similarly in other branches of physics.

If you claimed that there is an analytical formula for any quantity in the strong coupling limit, I think that this statement can be almost proven to be wrong. A lot of things are known about transcendentality of various expressions in gauge theory etc. These things have been mapped in quite some detail in thousands of papers. I don’t believe that any “revolution” described in simple vague terms as your last short paragraph can be made in 2009.

It sounds like finding an elixir of life. It is not clear what it is exactly supposed to mean and the many possible meanings that have been given to the phrase have been proven impossible. I just don’t know what you exactly mean so based on what you have written, I am surely not going to switch my brain into the mode that you have a 50% chance of making something that would deserve to be called a scientific revolution.

Doing work that would be competitive relatively to “generic” papers in gauge theory that I consider good would be good enough in my eyes while overhyped and unsubstantiated statements of someone who thrills other people by revolutions that don’t exist is not exactly my cup of tea.

Best wishes

7. Daniel de França MTd2 - January 5, 2009

What are glueballs?

Perhaps they are certain knot invariants found in QCD yang mills equations. I posted some articles about it here:


It seems Witten got his Fields medal working with these knots.


8. mfrasca - January 5, 2009

Dear Lubos,

Just an answer that I think also Dijkgraaf and Vafa, being good mathematical physicists, will appreciate:


Of course, generally speaking, solving a significant mathematical problem means also an important advance in physics. It is well-known since the first lessons at university that whatever physics you are doing you are solving differential equations. Nothing else. Given a way to solve them in a completely new regime is a revolution, and not only for physics.

It is anyway much interesting the number of prejudices that were built in qft and pervaded almost all physics. It is sad that you are providing them through string theory. We are at the point to accept as blatant what is not yet proved.



9. Luboš Motl - January 5, 2009

Dear Marco,

sure, solving a mathematical problem in physics is an advance. But you were talking about a scientific revolution. Every event that deserves this big label has to bring a paradigm shift, a new set of concepts and principles whose very existence was not previously understood and well-defined.

Solving a math problem that was well articulated before and whose answer was pretty much known simply cannot be a scientific revolution – quite generally. Almost by definition, this is what is referred to as the mundane, normal, everyday scientific activity.

I have absolutely no idea what you mean by “prejudices built into QFT”. In my optics, QFT is pure science. In fact, it is the most refined, accurate kind of science that humans have ever constructed and it describes all the non-gravitational phenomena that have ever been observed.

Pretty much everything that has to be included in QFT has been found and pretty much every unimportant or wrong myth that shouldn’t have been included into it has been eliminated. You seem to emit bombshell statements about the fundamental wrongness of the cutting-edge physics that are completely unsubstantiated.

Sorry but I include such statements squarely into the crackpot category. I am ready to discuss real physics, specific mistakes in some papers or improvements of physics that you are able to rationally justify by some evidence, but not this bombshell bullshitting that completely lacks any merit.

Best wishes

10. mfrasca - January 5, 2009

Dear Lubos,

The fact that you attach crackpot label here and there, mostly to your former colleagues, it is really a worthless matter. Of course, people belonging to scientific community may be more qualified for this.

When people spend a lot of resources to build supercomputers to solve equations otherwise not treatable with analytical means, and this is the most common case for physics and other fields, due to the fact that one does not have a small parameter to get a perturbation series, a shift to get such a perturbation series for a large parameter can be significant. Or not?

Of course, I am not claiming I have done a scientific revolution. There is no reason on Earth that I can think this. But it has been really interesting to stimulate you in this direction to obtain your standard reaction. And so I am happy to belong to the set of crackpots with a larger file of publications than you. And all this without you reading my papers on Physical Review and Physics Letters!



11. Daniel de França MTd2 - January 5, 2009

Edward Witten likes lattice QCD, and thinks it is very useful. See his most recent article, updated on January 3rd, 2009.


12. dorigo - January 5, 2009

Marco, the label you discuss is a coveted one, sort of a trademark of good science, when it is attached to one by Lubos. So you should be grateful to him for joining a large crowd of distinguished scientists 😉

I earned the label long ago, for my merits as a supporter of Peter Woit. Of course that was sort of a shortcut, since by consociating to PW is almost automatically going to earn one the status of crackpot. But I tried to be true to that grade since then.


13. mfrasca - January 5, 2009


As you read I have appreciated to be enlisted in such good company. Of course, you and Peter were the first two of the list to appreciate my blog and this cannot be underestimated.

Now, it will be my own responsibility to maintain the grade.



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