Will the LHC be able to test String Theory?

Definitely maybe.

String theory, the final theory, the mythical arbiter of truth heralding the end of science. Praised for its awe-inspiring beauty and elegance, string theory, like no other theory before, commands the attention not only of physicists but of the public too. String theorists have boldly gone where no man has gone before; they explored strange new worlds, 10^500 or so of them, most not hospitable to life. They brought us back extra dimensions, supersymmetry, and the promise to unify Einstein’s General Relativity with the mess that we call the Standard Model of particle physics. Let me correct that, they didn’t just bring a promise, they say they found it. And the one thing we all want to know is, are they right?

The Large Hadron Collider (LHC) explores energy ranges that no man-made experiment ever probed before, and it is just ramping up to reach out into the unknown again. The new run is an unprecedented opportunity to study the structure of elementary matter at shortest distances, down to a thousandth of a femtometer. Will it be able to tell us whether string theorists are right, and that fundamentally the world, you and I and our textbooks on loop quantum gravity, are made of strings?

Image credit: © WGBH Educational Foundation, via http://www.pbs.org/wgbh/nova/physics/conversation-with-brian-greene.html.

As so often in science, the answer is: It depends on exactly what you are asking.

String theory started out as an attempt to describe the strong nuclear interaction in the 1980s. And while it was quickly left behind by the more successful theory of quantum chromo dynamics (quarks, gluons, and all that), strings still play an important role in the description of the strong interaction. The “String Lund Model,” named after the Swedish town where it was conceived of, describes gluon interactions by flux tubes — the strings. Stretch them enough and the strings break apart into showers of secondary particles. This so-called “string fragmentation” is an integral part of many computer simulations which are necessary to obtain accurate predictions for scattering events at the LHC.

Images credit: Flip Tanedo of Quantum Diaries, viahttp://www.quantumdiaries.org/2010/10/22/qcd-and-confinement/.

The use of the String Lund Model has long been demonstrated and it isn’t really expected that the LHC data will tell us something new about it. Besides also dealing with strings, this model has little to do with string theory as we know and like it. The Lund Model is an approximation that supplements standard model particle interactions; it does not deal with the unification of gravity and the standard model, and it employs neither extra dimensions nor supersymmetry.

So what about the real deal then, the supposedly final theory that posits all our particles are strings in certain vibration modes, the theory with extra dimensions and supersymmetry and the endless arguments over its superiority to loop quantum gravity?

Image credit: Jeff Bryant, from Wolfram/Mathematica.

The strings can become excited to higher modes, which is a prediction specific to string theory and in principle observable. The energy necessary to make these excitations depends on the radius of string theory’s extra dimensions: The smaller the radius the larger the energy necessary to excite the strings. The most natural scenario puts the radius of the extra dimensions at the string scale: on the order of 10^19 GeV, give-or-take. In this case, testing string theory is hopelessly out of reach of the LHC, which reaches ~10^4 GeV at maximum, even with the recent upgrade.

In the case that string theory’s additional dimensions are quite large and in the range testable by the LHC, they would make themselves distinctly noticeable. The production of tiny black holes is one of the predictions. This process becomes possible because the extra dimensions make gravity on short distances much stronger than General Relativity with only three space dimensions predicts. For the same reason also the production of gravitons, the quanta of gravity, would become possible at the LHC if the extra dimensions were large. These phenomena give rise to specific observables that have been computed in great detail.

Image credit: Sabine Hossenfelder.

Additional dimensions by themselves would not tell us that string theory is correct, because this is only one ingredient of the full theory. However, if we were able to find evidence for extra dimensions it would speak very strongly for string theory and one also would expect true string phenomenology, that might reveal itself for example in string balls or fuzz balls, to be not too far away. Extra dimensions are the best-case scenario to test string theory at the LHC.

Physicists thoroughly scanned the previous LHC runs for signatures of black holes or graviton production that would speak for extra dimensions. They found exactly nothing. The possibility still exists that the somewhat higher energy of the upcoming run will deliver the sought-after evidence, which is a convoluted way of saying I don’t believe it but some of my colleagues refuse to give up hope.

Supersymmetry is another consequence of string theory that, when found, would strongly support but not directly confirm string theory. Supersymmetry predicts that all particles come in pairs. Since we have not found the supersymmetric partners of the particles we know of, supersymmetry must be broken so that the partner particles are too heavy to have yet been observed.

Image credit: DESY at Hamburg.

Before the start of the LHC, arguments that the partner particles should be within reach of the first run were wide-spread, an expectation based on the idea of technical naturalness, itself a hypothesis. But besides rumors, nothing was found. As in the case of extra dimensions though, it might still be that the next LHC run will produce the hoped-for signature.

How likely is it that the LHC will provide this support for string theory you want to know? Let me ask you in return: If you had a crush on Susy and she said she might come by after work, around 8pm, but she hasn’t shown up by 10, what are the chances she’ll be there by 10:05? Right. And them extra dimensions? Well, they never said they would come by, you just couldn’t exclude they wouldn’t.

Image credit: Matt Strassler, via http://profmattstrassler.com/articles-and-posts/some-speculative-theoretical-ideas-for-the-lhc/supersymmetry/supersymmetry-what-is-it/.

As teenager I wasted a lot of time waiting for men and resolved to learn from my mistakes. In my adult life I am much wiser. Instead of waiting for a man, I just happen to be so busy that I forget to leave without him. Along those same lines, string theorists in their adult life no longer wait for the final theory. In an interesting paradigm shift that has taken place in the community, they now consider string theory mainly a method to do complicated calculations within the standard model, a versatile tool to derive previously unknown relations. And they are very busy.

You see, that we know the Standard Model and can write down the theory is one thing. Being able to actually solve the equations to describe specific systems is another thing entirely. The methods typically used by theoretical physicists work very badly in situations where many particles are strongly interacting, such as in the quark gluon plasma created in collisions of large atomic nuclei (“heavy ions”) at the LHC. But in these situations, methods developed in string theory offer new solutions.

Image credit: Alfred T. Kamajian.

String theory helps with describing the quark gluon plasma by using the gauge-gravity duality that appears as a limiting case of a more general duality in string theory. The gauge-gravity duality can be used to map a difficult-to-treat strongly coupled system to an entirely different system that can turn out to be much easier to treat. In fact this duality has been used already to make predictions for the quark gluon plasma at the LHC, in particular for the energy loss of particles trespassing the quark gluon plasma.

And so scientific history turned back onto itself. String theory is again being used to describe nuclear interactions.

Unfortunately, the predictions from the string theorists did not agree very well with the data. The quark gluon plasma in the end doesn’t seem to be as strongly coupled as it was thought to be, thus moving it out of the regime where using the gauge-gravity duality would work well, or at least almost out. The LHC, thus, has already tested string theory!

Contrast of predictions from the string-theory derived gauge-gravity correspondence (orange line) with LHC data (black dots). Image Credits: Thorsten Renk. Details here.

In the next heavy ion run, that will probably take place towards the end of this year, more data will allow physicists to better explore the quark gluon plasma. The situation is not as clearly cut as it might appear at the moment because as a rule of thumb in heavy ion physics nothing is ever clearly cut. So who knows, maybe the gauge-gravity duality will get a second wind.

Does the use of string theory to describe strongly coupled phases of matter tell us something about its promise as a theory of everything? On the face of it, no. These are separate issues entirely: separate systems, separate tests, separate conclusions. However, many string theorists believe that since string theory is one theory that can describe quantum gravity, showing that it has some relevance to describe nature at all makes it likely it is the correct theory for the rest of nature too. That’s a non sequitur of course, but they almost certainly haven’t given up hope that string theory will eventually show up in some experiment. If not at the LHC, then perhaps elsewhere.

As the romance novels teach us, while you were dreaming of the supersymmetric princess, you would have been better off with the nice girl next door who was always there for you, the one who helped you sort out your strongly coupled problems. Maybe then physicists are eventually settling into a stable relationship with string theory, one in which reality replaces dreams. The LHC, then, will test how seriously they take their new commitment.