Of Particular Significance

A Prediction from String Theory

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 03/20/2022

(An advanced particle physics topic today…)

There have been various intellectual wars over string theory since before I was a graduate student. (Many people in my generation got caught in the crossfire.) But I’ve always taken the point of view that string theory is first and foremost a tool for understanding the universe, and it should be applied just like any other tool: as best as one can, to the widest variety of situations in which it is applicable. 

And it is a powerful tool, one that most certainly makes experimental predictions… even ones for the Large Hadron Collider (LHC).

These predictions have nothing to do with whether string theory will someday turn out to be the “theory of everything.” (That’s a grandiose term that means something far less grand, namely a “complete set of equations that captures the behavior of spacetime and all its types of particles and fields,” or something like that; it’s certainly not a theory of biology or economics, or even of semiconductors or proteins.)  Such a theory would, presumably, resolve the conceptual divide between quantum physics and general relativity, Einstein’s theory of gravity, and explain a number of other features of the world. But to focus only on this possible application of string theory is to take an unjustifiably narrow view of its value and role.

The issue for today involves the behavior of particles in an unfamiliar context, one which might someday show up (or may already have shown up and been missed) at the LHC or elsewhere. It’s a context that, until 1998 or so, no one had ever thought to ask about, and even if someone had, they’d have been stymied because traditional methods are useless. But then string theory drew our attention to this regime, and showed us that it has unusual features. There are entirely unexpected phenomena that occur there, ones that we can look for in experiments.

Forces that are Weak and/or Strong

The story begins with the strong nuclear force, whose connection with string theory I’ve written about before, for instance here and here. But the topic today is somewhat different.

The strong nuclear force, despite the name, isn’t always strong.  (“Strong” is meant in a relative sense; it is strong compared to the typical force at the same distance, as described here.)  The strong nuclear force is strong when measured at distances comparable to or larger than the size of a proton (a millionth of a billionth of a meter) and in subatomic processes with energy much less than the E=mc2 mass-energy of a proton.  It’s in this context that the strong nuclear force traps (“confines”) quarks, anti-quarks and gluons inside protons, neutrons and other “hadrons”, such as pions.  (A hadron is any particle made from quarks, anti-quarks and gluons.) But when collisions occur at much shorter distances and higher energies than this, the strong nuclear force becomes relatively weak: only a few dozen times stronger than electromagnetism at the same energy scale. 

This feature, called “asymptotic freedom,” makes the force (relatively) weak enough that we can think of quarks and gluons in high-energy collisions as nearly free particles that scatter off each other only occasionally, much the way we typically think of electrons and photons.  The 1973 discovery of asymptotic freedom in the theory of quarks and gluons won three of the physicists involved the 2006 Nobel Prize. The discovery of quarks themselves was made around 1970 (following suggestions of James Bjorken) under the assumption that asymptotic freedom was true. That discovery won the 1990 Nobel Prize; Bjorken didn’t win a Nobel, but was awarded the Dirac medal and a couple of other prizes.

Thus the strong nuclear force, as for any similar force that we might someday uncover in nature, shows different behavior in two distinct regimes:

  • At high energy and short distance, the force between particles is weak and the particles do not act as though they are confined.
  • At low energy and long distance, the force between particles is strong and the particles act as though they are confined.

Now, you might guess this is the general pattern; weak forces mean no confinement, and strong forces mean confinement.  It turns out isn’t actually the case. As was learned over the two decades following 1973, there can be strong forces without confinement.  For instance, a force could be strong and non-confining at high energies and short distances, while also being strong and causing confinement at low energies and long distances.

We haven’t discovered such a force so far.  But the forces we know today may be nowhere near the complete list, so we need, in our experiments, to be on the lookout for new forces, including ones that might have unfamiliar behavior. We need to keep our eyes out for a force of this type, whose quark-like and gluon-like states may still have strong forces even at high energy, and may never act at all like free particles that scatter occasionally — they may never be “asymptotically free.”

To illustrate this in the crudest way possible, I’ve drawn a cartoon below of these two possibilities.  Again, only one appears in the real world so far, but the other type of force might show up some day. 

The strong nuclear force is an example of a theory that is asymptotically free: it becomes weak at high energy and confines its quarks and gluons at low energy. A qualitatively different force would remain strong but non-confining at high-energy. Before the 1990s these were assumed to be the two main possibilities. One experimental distinction is illustrated in the circular insets: while for weak short-distance forces, a quark and anti-quark produced back-to-back lead to two narrow jets of hadrons, for strong short-distance forces one expects a larger number of wider jets, with a larger total number of hadrons.

How would we know we’d found such a force experimentally?  A key feature of real-world quarks and gluons is that a high-energy quark turns into a jet of hadrons, as I described here.  This jet is narrow; we see such jets all the time in experiments.   Now suppose we found a new force of nature, with its own quark-like, gluon-like and hadron-like particles.  If it is similar to the strong nuclear interactions, its hadron-like particles would appear in narrow jets.  But if it were strong at high-energy, then the corresponding jets of hadron-like particles would be more numerous and much wider than the ones we get from the strong nuclear force.  Exactly how wide and numerous these jets would be is hard to calculate, but we could try to make a rough estimate by extrapolating traditional methods.

All of this is stuff that was known as far back as the mid-1980s, and was applied to certain theories of the Higgs field in the context of “Walking Technicolor” (though I’m not sure when the experimental implications for jets were first emphasized; we were first thinking about the issues in 2001-2006.)  As far as I know, no one suspected there were any other possibilities.  But then in 1997, something new came onto the scene, emerging from mathematical realms of string theory.

Enter String Theory

In 1997, Juan Maldacena proposed that strings, when moving around on certain curved shapes with nine space dimensions and one time dimension, can be exactly the same as (that is, indistinguishable from) certain combinations of particles moving around in a familiar flat space with three space dimensions and one time dimension.

I’ve let Maldacena’s proposal be its own paragraph, because the incredible strangeness of his claim needs to resonate in the air for a bit.  We’re comparing two different types of objects moving around in completely different contexts.  The equations that describe them look utterly unrelated.  The strings come with gravity; the particles they’re equivalent to feel no gravity.  Even the number of dimensions is different. And yet, it is claimed, there’s a translation table between the two.  You can take any physical question in the string context and translate that question into the particle context, and vice versa.  And if you answer the string version of the question on the one hand, and answer the particle version of the question on the other, you will get exactly the same answer, even though none of the steps of the two calculations will look at all the same until the very last step.

An extremely crude cartoon of Maldacena’s proposal (sometimes called gauge/string duality) that string theory on an appropriately chosen 9-dimensional space (10-dimensional spacetime) is equal, in a non-obvious way, to an appropriately chosen theory of gluon-like and quark-like particles (along with some other particles) in flat 3-dimensional space (4-dimensional spacetime.)

This proposal, often referred to as “gauge/string duality”, is still not strictly proven. But there is an enormous amount of evidence now, and many cases in which the implications of the proposal are known to be qualitatively or even quantitively true.

A practical implication of Maldacena’s proposal is that there are certain extremely challenging questions about strings that can easily be answered by “quantum field theory” (the math we use for describing particles.) The reverse is also true: there are issues that arise in quantum field theory, and may even be seen in particle collisions at the LHC, for which the only path to an answer is through the math of string theory.

In exploring Maldacena’s proposal, scientists learned that among forces that have confinement, there is a third, qualitatively different class from the first two I mentioned.  We might refer to these as “ultra-strong forces”; I’ve added it to the cartoon below.   It’s ultra-strong forces which are most directly reflective of the physics of string theory. 

[The technical distinction between these three regimes involves the ‘t Hooft coupling αN, where α is the standard coupling strength, and N is the number of “colors” (i.e. versions) of each type of quark. In the three regimes, the ‘t Hooft coupling is much less than 1 (weak), close to 1 (strong), or much greater than 1 [but still less than N] (ultra-strong). Prior to Maldacena’s work it was more or less assumed that strong and ultra-strong forces were qualitatively similar.]

The Experimental Prediction

A prediction of string theory is that there is a third regime for confining theories, which I’ll call the ultra-strong regime. Production of particles in that regime (as well as the structure of hadron-like objects) is different from the other two. For a force that is ultra-strong, high-energy quark-like and gluon-like particles do not lead to jets, narrow or wide. Instead, their production leads to nearly spherical sprays, with no hint of jetty structure.

(I gave an intuitive argument for this, and discussed its experimental implications briefly, here. The argument was based on work I did in 2002 with the late Joe Polchinski, on hadronic structure in ultra-strong confining theories. Around the same time, Hofman and Maldacena made a similar but more confident claim, with a decisive proof that relies on gauge/string duality.   Another closely related paper appeared at the same time by Hatta, Iancu and Mueller.)

If the Maldacena proposal of 1997 is correct, as it appears to be, then there is an ultra-strong regime where confining forces are qualitatively different from those we previously imagined, both at low and high energy. String theory predicts that, among the unique features of such forces, production of quark-like and gluon-like particles would lead to near-spherical distributions of many hadron-like objects, each with low motion-energy, and that jet-like sprays will not occur.

Nowadays people call this kind of spherical spray by the cute acronym SUEP, for Soft (meaning lots of low-energy particles) Uncorrelated (meaning they go in random directions, forming a near-spherical spray) Energy Pattern.] We don’t understand nearly as much about SUEP theoretically as we would like — there are lots of subtleties to consider in realistic situations — so predictions for experiment are still quite crude. 

But experimenters at the LHC have this on their radar screen, and rightly so.  What’s really important is that this type of phenomenon, depending on its precise realization, 

  • could be thrown away by the trigger system and lost permanently, or
  • could be very difficult to look for because of the way LHC data is stored, or
  • could be buried unseen within the huge amount of LHC data. 

So even though a new force of this type, through its SUEPy signature (and variants of this signature, which I haven’t time to mention here), is just one of many possibilities that experimenters need to be looking for, it’s vitally important that they think about it carefully in advance. Otherwise they may inadvertently make it unnecessarily difficult or impossible to find, because of their assumptions on how best to gather, store, and analyze data. (An important theoretical paper looking at the trigger issues, by Knapen, Pagan Griso, Papucci and Robinson, appeared in 2016. Much more work remains to be done.)

The experimenters at the LHC have an interesting but tough job. There are dozens of possible novel phenomena that they need to be looking for in their data. Any one of them is a long shot; SUEP is no exception. But if it shows up someday, we’ll have string theorists like Maldacena (and many others, such as Igor Klebanov, Sasha Polyakov, Steve Gubser, and Ed Witten) to thank.  Without the years spent developing string theory’s mathematical underpinnings — without all that fancy supersymmetry and supergravity and extra dimensions and extremal black holes — those of us who make direct predictions for experiments wouldn’t even have known that SUEP was on the menu.

An apology: this is immensely oversimplified, for the sake of relative (!) brevity.  If enough readers are interested I can try to go into more depth at a later time, though this would require quite a few posts, not only on SUEP but on Hidden Valleys more generally.

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22 Responses

  1. Thanks for this Matt. I learnt something I did not know! In my approach to quantum gravity and unification, which is a pre-quantum pre-spacetime theory built on the non-commutative coordinate geometry of the octonions, the particle physics is a Left-Right symmetric extension of the standard model. The left-handed fermions have an associated U(1) charge which is identified with electric charge and the symmetries are just those of the SM. The right-handed sector has a U(1) charge which is interpreted as the square-root of mass (in Planck units). The associated symmetry is just the RH counterpart of the standard model: SU(3)_grav X SU(2)_R X U(1)_dark
    The SU(2)_R can be identified with Ashtekar’s formulation of GR; the U(1)_dark is a newly predicted dark photon (dark energy?). But I do not have any understanding of what SU(3)_grav…naively I assumed it to be weak like gravity, and confining like the strong force: thus providing a totally negligible correction to QCD. But could it be strong and non-confining; as predicted in string theory? I will greatly appreciate your insights. I should mention that my approach has lot in common with string theory: I have 2-branes evolving in 10D spacetime (equivalently an octonionic space). But I never compactify the extra dimensions; they are complex, and have an absolute magnitude of the order of the ranges of the internal forces. Quantum systems do not live in 4D classical spacetime, not even at low energies. Only classical systems live in 4D. Quantum systems always live in octonionic space; their description from the vantage point of a 4D spacetime is an (excellent) approximation, but fails to explain why the SM is what it is. The symmetries of the octonionic space coincide with those of the RH extension of the SM, thus bringing in gravity as well.

    Thanks and regards,


  2. Prof. Strassler:
    In the no-interaction Universe, I presume the quantum fluctuations of each quantum field would not be influenced by any other quantum field. However, is that the case in our Universe? Are the quantum fluctuations in a given field different in the vicinity of a particle of another field than they would be if no particle were present? Can the quantum fluctuations of one field interact with the quantum fluctuations of other fields, act on and be acted upon?

    In the no-interaction Universe would any particle have mass? Could the Higgs boson have mass by interacting with itself? Because no other quantum field would interact with the Higgs field, their quanta would be massless. And if they were massless always travel at the speed of light. So there would be a charged, massless electron with the charge having no dynamical effect.

    Would condensed matter be possible in the no-interaction Universe since some exchange forces are attractive?

    Finally it would seem such a Universe would be absolutely homogeneous and non-evolving with the number of particles determined by the initial conditions of the Univerese.

    If you have time, many thanks for answering my questions.


    1. When an electron in an atom absorbs a photon, that is a quantum of one field interacting with the quantum of another field. Quantum fluctuations of interacting fields also affect one another, and though the effects are often small they have often been measured, as in “g-2” of the electron and also of the muon, in which the quantum fluctuations of the photon field and electron field interact and create some of the many small shifts to g-2, for example figure (c) in https://satrasarticocos.files.wordpress.com/2017/02/anomalous_tot.jpg?w=680 .

      Interactions are not needed for some types of particles to have mass. However, a particle could not get mass from a Higgs field unless its field interacts with the Higgs field. If the interaction between the Higgs field and other fields were turned off, then yes, the electron would be charged but massless.

      Certain types of condensed matter would be possible in principle without interactions, such as a Bose-Einstein condensate, but there would be no way to prepare or contain it without interactions.

      Without interactions all particles move in straight lines and that is the extent of the evolution of the universe. But the universe need not be or become homogeneous; that depends how it starts out.

      1. Prof. Strassler:
        My understanding of quantum field theory at the qualitative level has gone up many hundred percent from your last three posts. Parts from “Quantum Field Theory for the Gifted Amateur” have fallen into place. Somehow, in a wonderful way, a description in words makes the math less arcane.

        And a bit of cosmology as a lagniappe.

        Many thanks, Rick

  3. Prof: Strassler:
    In a Universe without forces/interactions could the quantum fields which produce the forces/interactions in our Universe exist? If so, then they would have vacuum fluctuations and these fluctuations could influence the matter fields.

    Also, even without the five fundamental forces/interactions would not exchange forces exist?


    1. Free quantum fields (i.e. without interactions) make sense, yes. And their particles have exchange “forces”; you can put free photons into a laser state, and you could not put two free electrons into the exact same state. But of course, as free particles, these photons and electrons don’t actually do anything except travel in straight lines and pass through each other.

  4. Prof. Strassler:

    Certainly does, thank you.

    I would be most interested to read your explanations using examples but realize you are busy and perhaps the explanations would require a level of mathematical knowledge inappropriate to this blog. For myself, with considerable intellectual perspiration I can follow the math in Feynman’s Lectures on Physics Quantum Mechanics. Like drinking out of a fire hose.

    In one volume Feynman describes watching games of chess as an analogy to doing experimental physics. From carefully watching the moves of the pieces certain rules about their movements can be deduced. It struck me that an analogy to the Pauli Exclusion Principle could be deduced from moves that are never made. Specifically, that a piece of a certain color never moves to a square already occupied by a piece of that color. Thus, no square can contain more than one piece of the same color.

    Is it not true that the fundamental laws of physics, whatever they ultimately may be, have no deeper “explanation”? The explanation is simply, “That is the way Nature works.” Historically what was thought to be a fundamental law may turn out not to be so, but unless the chain of laws is infinite there is a stopping point.


  5. Prof: Strassler:

    As usual a thought provoking discussion.

    I am trying to get my head around the phenomena at play. One is that due to the wave like aspect of all quantum particles their kinetic energy increases with decreasing distance. If I understand correctly a change in energy with distance generates a force, conventionally termed at the atomic and sub-atomic levels an interaction. Another type of interaction, as you have so clearly explained, is that the presence of one quantum field causes a “disturbance” in other quantum fields, this disturbance given the conceptually most confusing name of exchanging virtual particles. The Pauli Exclusion Principle prevents more than two particles with spin from being in the same state. Undoubtedly true but always has been as or more mysterious to me as virtual particles were. But it would seem the Pauli Exclusion Principle is another type of interaction. Finally the ever present quantum fluctuations which, if not a fundamental interaction in-and-of themselves, modify the “fundamental” interactions.

    It is some combination of the interactions I have stated that are in-play or others, or something else, or am I completely out-to-lunch.

    Many thanks for any enlightenment .


    1. You are right that quantum physics itself, though the uncertainty principle (kinetic energy versus small size, quantum fluctuations of fields) and the Pauli exclusion principle for fermions (and the corresponding though reversed effect for bosons), has an impact on both isolated objects and on identical nearby objects. These are somewhat orthogonal, however, to the “four forces” that physicists talk about (gravity, electromagnetism, strong nuclear, weak nuclear, and Higgs — oh, right, there’s really five.) One way to see this is that even if all the “forces” were switched off, so that all particles were “free” to roam independently, they would still be subject to these quantum physics rules, which are prior even to forces. Does that help? It’s not so easy to explain without examples…

  6. Could you explain what is going on at the origin of the Maxwell–Boltzmann statistics?

    When people start talking about the strong force, I keep going back to the Maxwell–Boltzmann statistics chart and wonder if the attraction, strong force, is due that the fact there is more “space” at the nucleus to accommodate the “particles/fields”, hence a jam, a lock, “confinement”. The energy required to free the particles would then be higher than the peak shown by the Maxwell–Boltzmann statistics.

    Does this make any sense?

    Great article, thank you.

  7. You mentioned the mathematical realms of string theory but much of advanced modern physics is distant from the mathematical approach and cannot be rigorously proven. Since Feynman there is also a not even too hidden division between mathematicians and physicists and they tend to talk past each other.
    It’s also a sad coincidence that you are coming back to fundamental physics in this international situation. If I never saw real world applications of string theory, now more than ever I’m afraid that the only terrible application of high energy physics has always been in the military field.

    1. There’s a long history of back and forth between mathematicians and physicists. Sometimes math moves ahead of physics in one area, and sometimes the reverse is true. As far as I can see, the main problem with proving things in modern physics rigorously is the difficulty of quantum field theory; math has not caught up with that. But supersymmetric quantum field theory is kind of in between; it has some of the same features as the real world quantum field theories we observe in experiments, but it also has relative mathematical simplicity, so it gives us an opportunity, every now and then, for proofs of greater or lesser rigor.

      Regarding “applications,” that’s something completely different and unrelated to “predictions”, which can be immensely useful in a different sense. But if you want to talk about applications, then when it comes to elementary realizations about the world, the time for applications is often 50 to 100 years or more. What was the practical application of discovering Jupiter has moons, Saturn has rings and the Moon has craters? Are we to say that Galileo’s discoveries are diminished by the fact that we have never put those rings to human application?

      Arguably general relativity hasn’t had an application yet; even its role in GPS is just to provide a correction to a more basic technological idea. Of course, quantum mechanics arose at the same time from these same explorations, and the applications to modern life are beyond count. So the idea that string theory ought to have real-world applications is ahistorical; some ideas are valuable right away, some centuries hence. I doubt the discovery that galaxies are millions of light years away will have much application ever.

      As for high-energy physics of 50-100 years ago, it certainly has some applications by now, and they’re hardly limited to military use. Regarding high-energy physics of today, I’m too wary of history to make any predictions about how it might be useful… nor am I concerned, remembering Galileo’s planetary discoveries, since the value of discoveries is not measured purely by their utility.

  8. It would be interesting if string theory applied to spontaneous parametric down conversion, “Entanglement”. And the possibility of communication with the effect.

  9. Great article, question if I may. The strong nuclear force is an attractive force. I realize that the “strong nuclear force” resides inside the proton and neutrons, binding quarks, with the residual strong nuclear force binding the protons and neutrons in the nucleus of the atom. Does the strong nuclear force ever become repulsive? In other words, if I try to squeeze two protons or neutrons closer together in the nucleus, the repulsion that occurs, is that a result of the Pauli Exclusion Principle or does the Strong Nuclear force itself become repulsive?

    1. Hmm… I think these are two separate issues. The strong nuclear force *can* be repulsive, see for example https://www.ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QCD/SimpleExample_1.html https://www.ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QCD/SimpleExample_2.html
      However, I don’t think these issues play a role in the proton-neutron potential energy. If I remember correctly (and I should emphasize I’m not a nuclear theorist, and I might be misremembering) the repulsion between a proton and neutron does involve the Pauli exclusion principle for the quarks interior to them. [Experts, please set me straight if I’m off base here.]

      1. I’m pretty sure that’s the case; nucleons of a kind pair up with opposite spins, much as electrons int heir shells do, and indeed form shells that give us the ‘magic numbers’ of nuclear physics. I’d be surprised if that was a strong force effect.

        1. I don’t think that’s quite the same issue. The quantum numbers of hydrogen aren’t an electromagnetic effect, but the electron-nucleus potential is still entirely attractive for the innermost shell.

  10. Enjoyed this very much. My dad Mel Schwartz co-discovered the muon neutrino in 1962; he died in 2006, and would have been fascinated with the way these theoretical developments have proceeded since then. And I am sure that Fermi, about whom I wrote a bio in 2017, would be intensely interested, since he was deeply interested in the issue of nuclear forces and interaction. Anyway, great piece. Thanks!

    1. Thanks for your comment and kind words. I remember your father, having heard him speak and having met him once, probably around 1990, when I was a student at SLAC. He was a huge figure in the field, that’s for sure.

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