Friday, December 21, 2012

Large Extra Dimensions - Not Dead Yet

15 years ago large extra dimensions were on vogue.

The idea that our universe may have additional spatial dimensions so small we have not yet been able to observe them dates back more than a century. This idea received a tremendous boost by the realization that String Theory actually requires such additional dimensions for consistency, but they were normally assumed to be wrapped up to sizes about a Planck length, or 10-35m. That’s so small you can forget about it. (Forgetting about them being the reason to wrap them up to begin with.)

Then in 1998/99 some smart physicists realized that if there are extra dimensions, they could be much larger than the Planck length, and we wouldn’t have noticed. Better still, if these dimensions have the right size this would explain why gravity is so much weaker than the other interactions in the standard model, a problem called the “hierarchy problem” that causes physicists sleepless nights.

In these scenarios with large extra dimensions, the stuff that we are made of (quarks, electrons and so on) sits on a slice with three spatial dimensions, which is called a “brane”. This matter does not normally notice the additional dimension, but gravity does. This has the result that gravity is weak on long distances, but becomes much stronger on short distances, leading to a “lowered Planck scale” and quantum gravitational effects that are much larger than naively expected. Thus the excitement. (There are different models with different realizations of this, but the details won’t concern us in the following. For details read this earlier post.).

If one buys into this, one however has a new problem: The question why the extra dimensions have exactly this size. But sometimes finding a new way to formulate an old question can be a big step forward, so this should not deter us from exploring the idea.

Models with large extra dimensions also made predictions for the LHC due to the lowered Planck scale, most strikingly graviton and black hole production. In 2012, now that the end of the world is near, we know that nothing like this has been seen.

As I explained in this earlier post, it is quite rare that experiment can falsify a model, even if you might have heard so. Normally a model has free parameters that should be determined by experiment, or, if nothing is found, be constrained by experiment. That the LHC has not found evidence for large extra dimensions doesn’t falsify the idea, but it certainly “implausifies” it by constraining the parameters into an uninteresting range. Which is another way of saying, move on, there’s nothing to see here.

So you might think large extra dimensions are dead. But Cliff Burgess begs to differ. In two recent arXiv papers, he and his collaborators have put forward an extra dimensional model that offers an intriguing new perspective:

    Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction
    C. P. Burgess, L. van Nierop, S. Parameswaran, A. Salvio, M. Williams

    Running with Rugby Balls: Bulk Renormalization of Codimension-2 Branes
    M. Williams, C.P. Burgess, L. van Nierop, A. Salvio
The key point is that they are trying in the first place not to solve the hierarchy problem, but the cosmological constant problem: Why is the cosmological constant that we observe small and nonzero? The cosmological constant term in general relativity describes the energy of the vacuum and this energy should receive contributions all the way up to the Planck energy. This would be a huge contribution, leading to a very strong curvature of our universe, incompatible with observation. Why aren’t these Planck energetic quantum contributions there?

Burgess and his collaborators argue that a plausible reason is that space-time has additional dimensions, and the full space-time is not Lorentz-invariant. In other words, it’s a scenario with branes in higher dimensions. In such a situation, the troublesome quantum contributions, which normally, due to Lorentz-invariance, take on the form of a cosmological constant term, might not make themselves noticeable on the brane, which is where we live.

The example that they give is that of a cosmic string. If one calculates the metric that the string induces, one finds that space is flat but has a defect angle that depends on the string tension. The string itself however is unaffected by what it does to the background. The scenario that Burgess et al construct is basically a higher-dimensional version of this, where our universe plays the role of the string and creates a defect, but no curvature is induced in our universe itself.

Concretely, they have two additional large extra dimensions. (There might be more than that, but if they are much smaller their presence does not matter for the argument.) These additional dimensions have the topology of a sphere. On the two poles of the sphere, there are a brane each, one of which you can interpret as our universe. Like in the case with the cosmic string, the matter density on the branes induces a defect angle for the sphere, creating a manifold which they call a “rugby ball”. The radius of the sphere is flux-stabilized, which leaves one free parameter (a combination of the radius and the dilaton field).

These extra dimensions induce a vacuum energy on the brane, which is essentially the Casimir energy of this compact space, and this energy depends on the radius of the sphere. To use this scenario to get the right value of the cosmological constant, the radius should be of the order of about 5 μm, which is somewhat below current measurement precision (45 μm), but not so far below.

But what about the troublesome quantum corrections?

Supersymmetry must be broken on the brane (because we don’t see it) but is intact away from it. Supersymmetry solves the cosmological constant problem in the sense that it brings all the troublesome contributions in the bulk to zero. What remains to be shown though is that the cosmological constant on the brane does not receive large correction terms, which depends on the way the branes are coupled.

Cliff and his collaborators have shown that, in the scenario they constructed, the cosmological constant on the brane (read “in our universe”) does receive correction terms from high energies, but due to the way the branes are coupled these corrections are highly suppressed and do not ruin the smallness of the effective cosmological constant; they do not induce a large curvature. Think of the example with the cosmic string that stands in for higher dimensional branes. The geometry on the string (or brane) is flat regardless of the value of the tension. The large quantum corrections are there, but they contribute to the tension rather than inducing a curvature.

Now once you have fixed the radius of the “rugby ball” so that the cosmological constant matches with observation, you can use this to calculate the value of the lowered Planck scale. It turns out to be at least 10 TeV, so we wouldn’t see gravitons or black holes at the LHC. (Keep in mind that the LHC collides protons, which are composite particles. The average energy per individual collision of quarks or gluons is in most cases far below the total energy in the proton collision which is usually quoted. That’s why everybody wants a lepton collider.) However, since the string scale is somewhat below the Planck scale, one would expect to see string excitations at the LHC, though still at fairly high energies; we wouldn’t have seen them yet.

So to sum up, what this model achieves is the following: 1) It provides a setting in which there is a small cosmological constant whose small value is not ruined by large quantum corrections. 2) It makes the prediction that we should see corrections to Newton’s law not too far beyond present measurement precision. 3) It gives a plausible reason why we haven’t seen evidence for extra dimensions at the LHC so far but 4) predicts that we should see some glimpses of it in form of string excitations within the next years.

This doesn’t convince me to start working on large extra dimensions again, but it does convince me that large extra dimensions aren’t dead yet.


  1. Hi Bee,

    Thanks for the nice explanation of the Cliff Burgess et al proposal. In as the LHC is scheduled to be cranked up to 13 TeV after an extensive shutdown I’m wondering if this is when such extra dimension effects might be expected to show up?



  2. Well, the flat space is three dimensional by definition. How many dimensional is the curved space, after then? And how many dimensional such curved space will get, when it's curvature gets curved?

  3. /*In 2012, now that the end of the world is near, we know that nothing like this has been seen...*/

    Because the end of old world already passed, it's time to admit, that every gravitational lensing, refraction and polarization of light, every force violating the inverse square law is the manifestation of extradimensions of flat 3D space.

  4. Bee,

    When you say string excitation, do you mean superstrings or cosmic strings. I assume the former but didn't want to guess wrong.

    The model says that it lowers the string scale from Plank level, does it mean that superstrings actually(if the model is confirmed) do their work above Plank scales, not at it?

  5. Zephir:

    "Well, the flat space is three dimensional by definition."

    Which flat space? Which definition?

    "How many dimensional is the curved space, after then?"

    As I wrote its 2 additional dimensions. 2 plus 4 is 6. There could be more as long as they are small enough, well, read what I wrote.

    "And how many dimensional such curved space will get, when it's curvature gets curved?"

    I have no clue how you want to curve a curvature. Best,


  6. Hi Phil,

    It's not so easy because, as I wrote, the 13/14 TeV are per proton collision, not per parton collision (a parton being a proton constituent). It is, simply speaking, very unlikely that 13 TeV go into a single parton collision. Exactly how unlikely depends on the "parton distribution functions". Basically, it's not enough to crank up the energy, you also have to wait for sufficiently many collisions to get sufficient highly energetic events. All of which is to say, I don't know how long it will take... Best,


  7. Hi Alexander,

    Yes, the former. The string scale just is not identical to the Planck scale. Best,


  8. End small dimensions with calculated versus measured Rydberg formula or hyperfine transition (e.g, 21 cm line for hydrogen) for a high-Z hydrogen-like atom (re HITRAP). Correct for spin-orbit interaction, non-point-charge nucleus plus small s-electron orbital radius giving a less than Z effective potential, and relativistic correction: Curium-248, nuclear spin = 0, half-life 348,000 years (alpha-emitter), 30 - 50 mg/year production.
    nuclear Radius = rA^(1/3); r set from gold

    For [Cm-248](-95): [6.6742×10^(-11) m^3/kg-s^2][4.1185×10^(-25) kg]/[7.88×10^(-15) m]^2 = 4.427×10^(-7) m/s^2 or ~4.43x10^(-5) cm/s^2 gravitational acceleration at the nuclear surface. A 1s electron has an antinode at the nucleus. A small dimension will seriously change Big G, shifting transition energies.

    "No theorist left behind" is execrable. Observe then cull.

  9. /*Which flat space? Which definition?*/

    That's the good question - because even the seemingly empty space contains minuscule deforms: CMBR photons with their spin-1 and spin-2 components. So we have another example of extradimensions in vacuum fluctuations (after all, in the same way, like the Brownian noise at the 2D water surface would serve as an evidence of third dimension of the underwater).

    But in general, the "flat, just 3D" is just the space, which doesn't exhibit any forces and/or lensing - both microscopic, both macroscopic ones. Which is indeed an abstraction, but the physicists are using it routinely. When the space is curved, they attribute it to another, time-like dimension.

    /*I have no clue how you want to curve a curvature.*/
    With differential concept. Gradient requires the presence of 1st derivation, its gradient is the 2nd derivation and so on...

    BTW Merry Christmas to You and your family.


  10. If one brane is our universe then what is the other brane? And can gravitational influences go from one to the other?


  11. Sort of undead physics?

    Or maybe the living dead that cannot be killed scientifically?

    Whatever sticks to the wall?

  12. Zephir,

    So first you bring up some flat 3-dimensional space and then you don't know which space you are talking about? Could you please stop making such pointless comments then?

    Also, let me summarize the breadth of your knowledge about differential geometry: One curves a curvature with differential concept. I think you have a somewhat confused understanding of this, maybe go back to the books. Best,


  13. ppnl,

    Could be another universe or, if the wrapping of the branes is more complicated, who knows, maybe it's the same. In any case, yes, they should influence each other gravitationally. This is the same, really, as with all the other braneworld scenarios. Best,


  14. Kind of like the way the years have gone by and your dealing with the issue of extra-dimension.:)

    I am still the incurable hopeless romantic about what we can see and what I suspect we don't see.....but that is not very kosher with the science is it?:)

    In the one sense, a very abstract theoretical idea about what can be married to "real life in nature's expression of the cosmos....yet," what is it that propels the universe to be the way it is if we do not extract observable decay chains? What is the essences of what nature has revealed in cosmological correspondences, as evidence in the backdrop measures here on earth?

    The calorimeters define for us the energy decimation of collision process, but it still does not all add up energy wise? So many collisions, so many energetic values that are still missing? I don't really know, and am still speculating?

    A sugar cube, and the space in between? Displacement, as a teaspoon measure in a fluid finds room for, and does not raise the level. Archaic indeed :) A zipper, still exists that allows one to step through the veil of the illusions I may still perpetuate?

    Save me:)

  15. Thanks for explaining the key ideas of these interesting models in a nice and understandable way here.

    I like this.

  16. So if gravitation travels between branes and that other brane is so close then couldn't it be a good place to hide dark matter? Gravitationally it is there but it is 45 μm away in the wrong direction.

  17. >does not matter for the argument

    I was looking for Smolin's new book - still as elusive as the dimensions in string theory apparently - your blog mentioned it in 2010 and then I clicked on the masthead for the latest post, hence I arrived at this point in time. I'm not paid to be a scientist or philosopher so perhaps my perspective doesn't count but in my humble opinion if you have to take something on faith then it isn't science it's religion and I'm a non-believer. If you exclude something however inconsequential you may deem it to be, or indeed invent something to help explain away an inconvenience in a theory, then you are writing fiction, not fact. I think this is the reason people in the USA (and I mean the 94% who believe in some preternatural entity, practically the whole country if we're disregarding elements that do not matter for the argument) have such a hard time with "science" in the 21st Century (we'll exclude the pathologically insane argument, as after all, religion is a by product of evolution, so it's really not their fault...)

    My chem teacher says K.I.S.S. Now I know science is inherently complicated, but I think explaining fact by inventing fiction, or negating existing facts, is a blind man leading the blind - you may all think you know where you are going buy you're just swimming around in your own little bowl. The future needs science to be the biggest fish in the biggest bowl if we are ever hoping to get out of the 21st Century with our lives and our dignity.

    Happy Holidays!

  18. Hi Ppnl,

    people have played with this idea a decade or so ago. You don't need the specific model that Cliff proposed for this, a vanilla ADD model will do. The brief summary is that it doesn't work because dark matter isn't just dark: It isn't distributed like it was normal matter that we just don't see. Its distribution is correlated with that of normal matter. It is essential to structure formation. It doesn't interact with itself the same way that our normal matter interacts with itself either. I also don't think the scales work out if you put in the numbers but can't recall the details. Best,


  19. Sometimes I'd really like to be able to downvote or flag trolling comments, such as the one of "emilycurious" for example ...

    A feature similar to the one of Amazon, which allows one to ignore comments of specific people, would be helpful too to filter for the interesting contributions to the physics discussion and ignore the crap.

    Can something like this be done here?

  20. "Nemo", are your comments somehow more valid than anyone elses? Is this really how we wish science to be conducted in the 21st Century, by elitists?
    I have no idea why my opinions should be labelled "trolling" any more than your tantrum.

    I'm sure I'm not as intelligent or as well read as you, yet, but I'm more than prepared to stand on the front line of science and take on any naysayers from within or without.

    Defend your science, don't run away and hide behind anonymity and baseless accusations.

  21. Nemo: No, unfortunately Blogger doesn't have such a feature. (Btw, it seems that discussion to my blogposts is more and more moving over to facebook, mostly because the comment feature is less cumbersome.)

  22. emilycurious: Your comments are entirely off-topic. Since you seem to be new, please read the comment rules. If you have more off-topic comments I'll delete them. Best,


  23. Thanks Bee for responding,

    so I'll have to ignore comments of people, who too often have nothing constructive to say, just by remembering their names and not reading these comments ...

    For me it is a bit unfortunate that the more interesting and nicer discussions take place on facebook. I highly distrust facebook, so I'll most probably not be able to read the discussions there, if I dont want to register. Or is there a way to (at least passively) take part for not facebook-registered persons ?

  24. Nemo: You'll have to register. That's why the comments work so well. Blogger seems to be falling behind in many ways at this point, one can only hope that they're working on an update. (That would include, eg, the option to rate comments.)

  25. Bee,

    Yes but if gravitational influences cross branes then matter should clump over there in the same places it clumps over here because of that interaction.

    Also maybe the rules are different over there. Maybe the other brane is a kind of dual universe with supersymmetery particles rather than normal particles. So their particles will not interact with each other or with our particles.

    Now maybe this is chaining a lot of maybes together but if two branes are close together it seems like they should leave a gravitational imprint on each other.

  26. A crib sheet baseline for the generalities "beyond the brain theories?":)


  27. As well, some familiarity with the subject for sure.

    Even the many theorists who are interested in how string theory connects to the real world don’t typically think much about what it means to test the theory. Fortunately, an increasingly active group of “string phenomenologists” are focusing on formulating a string-based description of the world and testing that understanding. They are already making testable predictions, and will increasingly do so.String Theory and the Real World by Gordon Kane


  28. So... we have models with extra dimensions!

    Some Models with some dimensions that did not expand.

    1. Are there models that analyse the conditions that could exist with all the dimensions at minimum length?

    2. Are there models that assume that all dimensions were bigger than our 3d space/time and that our 3d space time has shrung to its present size?


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