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Here and on many other forums and blogs people ask the question "What if LHC does not find SUSY?". I would like to ask the opposite. What if it finds it? What would the implications be? Is it going to just confirm something understood and expected or is it gong to bring something new? Will there be implications for string theory? String theorists will take it as a good sign, but by itself it is not a confirmation of string theory.

I do realize this is more that one question, but they are on the same topic.

p.s If this question is not suitable for this site, please delete/close

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MBN
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    We change the "What next?" language in our grant requests. – dmckee --- ex-moderator kitten Mar 07 '11 at 16:46
  • @MBN I remember lectures in supersymmetry back in the eighties and the justification was that it made computations finite, nothing about strings. I guess it is history in retrospect. The thesis of my doctorate ( experimental) dealt with Regge poles but it is from Lubos I first heard the string connection. – anna v Mar 07 '11 at 18:25

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An even more excellent question than the opposite one!

Experimenters' job

The first happy group of people for whom the discovery of SUSY at the LHC would be spectacular would be the experimenters. They would experience fireworks of activity, facing the task to find as many superpartners as possible and to measure their properties.

All their masses - and several other parameters - would be news for the theorists. We would have to learn lots of new, currently unknown numbers from the experiments, the so-called soft SUSY-breaking parameters. It's conceivable that the masses would display some patterns - e.g. mass ratios - that agree with one of the scenarios of supersymmetry breaking. So some of the mechanisms of supersymmetry breaking would be supported; others would ultimately be abandoned.

Figuring out the logic of SUSY breaking

Quite a lot of data is needed from the first hints of SUSY to the point in the previous paragraph because one needs to see many new particles and some of them are inevitably harder than others. However, if this job is completed, we will know whether SUSY breaking is mediated by gravity mediation, anomaly mediation, gauge mediation, mirage mediation, or something else.

It would be a lot of interesting work for the theorists and it is more likely than not that they have already done the essential work for any major type of SUSY breaking that could be observed by the LHC. Obviously, one of the schemes would be studied in much more detail if we knew that it is the correct one. Some knowledge about the mechanism of SUSY breaking - which may be guessed from the superpartner masses - would tell us a great deal about the required underlying compactification of string theory etc.

Also, the role of the newly found SUSY for all the problems that SUSY is capable of solving - that have been discussed under the question

What if the LHC doesn't see SUSY?

(I mean dark matter, gauge coupling unification, and the hierarchy problem) would be studied in much more detail, too. I don't have to enumerate them again because this text would become highly redundant. It's obvious that if the existence of low-energy SUSY were supported by the experiments, all other things that were expected to be solved by SUSY would be studied much more seriously, much more materially, and in much more detail. Some of the advantages of SUSY are only understood superficially - this situation would have to improve.

LHC SUSY discovery and string theory

The discovery of SUSY would be amazing - the first discovery of a new spacetime structure and symmetry since Albert Einstein's relativistic adventures. It would be great, it may happen, and string theorists must be ready to take credit for it. No doubt, at least in the Western (non-Soviet) context, SUSY is a daughter of string theory. First, it was discovered by Pierre Ramond on the 2-dimensional world sheet of a string, before it was exported to the 4D spacetime and other higher-dimensional spacetimes and before it was found in the 10D spacetime of superstring theory as well. Historically, supersymmetry was one of the first amazing ideas that the physicists were forced to discover because string theory led them to discover them.

All the critics of string theory would be proved to be spectacularly wrong - in fact, narrow-minded folks who wanted to prevent the mankind from discovering one of the most fundamental properties of Nature; everyone could suddenly see that they are on par with the geocentrists and they would hopefully never show up again in the public. I would win a USD 10,000 bet against a phenomenologist who agreed with 100-to-1 odds - this "uneven" number itself is enough to show that some of the enemies of supersymmetry resemble a fundamentalist religious sect.

The pragmatic and largely non-anthropic phenomenological attitude to string theory would prevail. People would probably agree that a feature of the vacua doesn't have to be "generic" for it to become true. The anthropic principle would fade away. Because low-energy SUSY would become a fact, people would kind of accept that with some extra knowledge about the reality used as assumptions, supersymmetry is a consequence of string theory. See

http://motls.blogspot.com/2010/06/why-string-theory-implies-supersymmetry.html
Why string theory implies supersymmetry

Lots of knowledge about the likely compactification of string theory would become much more accessible. String theorists - which would become a quickly growing group - would very likely converge to some opinion whether heterotic string theory; heterotic M-theory; M-theory on a G2 holonomy manifolds; type IIA intersecting braneworlds; or F-theory on Calabi-Yau four-folds is the most viable approach to phenomenology.

I have discussed in what sense string theory probably implies supersymmetry. Now, you're obviously interested in the opposite hypothetical implication - whether supersymmetry implies string theory. We can't prove this implication as a mathematical theorem but it would become extremely persuasive. First of all, supergravity (SUGRA) would become an inevitable component of all effective field theories because it follows from general relativity (established) and supersymmetry (hypothetically established in our thought experiment).

In this text,

http://motls.blogspot.com/2008/07/two-roads-from-n8-sugra-to-string.html
Two roads from N=8 SUGRA to string theory,

I argue that supergravity suffers from two kinds of problems: non-perturbative inconsistencies; and the unacceptable phenomenological limitations of its maximally supersymmetric N=8 version (which is the only perturbatively finite one). Attempts to fix either of those limitations of supergravity inevitably leads to string theory with its more powerful toolkit. If you want to watch a 30-minute lecture by a Dirac Medalist explaining why supergravity can't be decoupled from string theory and why one needs all of string theory to preserve the consistency, see this November 2010 talk by Michael Greene in Trieste:

http://www.youtube.com/watch?v=UVqCAhLiZDc
http://www.youtube.com/watch?v=S8wSl2R3G1o

Similarly, in the text a few paragraphs above, I argue that locality of general relativity implies that there must exist magnetically charged objects - at least black holes - and the Dirac quantization rule implies that the charges must belong to a lattice. The choice of the lattice is equivalent to the point of the moduli space of inequivalent stringy vacua; the noncompact symmetry group of SUGRA is inevitably broken down to its discrete exception subgroup, the U-duality group. In the appropriate limits of the moduli space of the inequivalent vacua, we may derive the existence of objects known from string/M-theory as well as their excitations, and we may pretty much complete the rest of string theory by consistency arguments.

Green-Schwarz anomaly cancellation

There is one more characteristically stringy structure that would become necessary if we add one more assumption: the Green-Schwarz mechanism that mixes tree-level terms with one-loop terms in a very stringy way - originally discovered by Green and Schwarz in 1984 when their discovery sparked the first superstring revolution.

This mixing of contributions at different orders is extremely unnatural in perturbative field theory. And we would have evidence that it takes place in Nature assuming that there exists at least one axion - or, in SUGRA terms, at least one linear supermultiplet. If there are axions, which may be needed to solve the strong CP-problem, there are also new kinds of anomalies (in particular, the "conformal anomaly" of supergravity) analogous to the 10-dimensional anomalies addressed by Green and Schwarz in 1984. A 4-dimensional version of the stringy Green-Schwarz mechanism would be needed to cancel those anomalies.

Theorems may be rigorously proved in the highly symmetric vacua only but not in the real world. However, in the real world, the evidence that string theory is right would become overwhelming.

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Luboš Motl
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    How would all critics be proved wrong if susy does not imply string theory? – TROLLHUNTER Mar 07 '11 at 17:42
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    It does under extremely mild assumptions. Please read my answer. Also, one of the reasons why it does - that I sketched - was also discussed in a 30-minute talk by Michael Green in Trieste - lectures of the Dirac Medalists. See http://www.youtube.com/watch?v=UVqCAhLiZDc and http://www.youtube.com/watch?v=S8wSl2R3G1o – Luboš Motl Mar 07 '11 at 17:43
  • +1, thanks. As usually you take the questions seriously and give detailed answers. Corrected me if I am wrong but doesn't SUSY predate string theory, and what do you mean that it is a daughter of string theory? – MBN Mar 07 '11 at 17:57
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    Dear MBN, because SUSY is daughter of string theory, it can't predate it: the reason is known as causality. ;-) In the Soviet Union, mathematical physicists actually found supersymmetry as a generalization of the spacetime symmetry groups. In the West, as I mentioned, supersymmetry was born in Pierre Ramond's project to incorporate fermions into string theory. He turned the old bosonic string theory to superstring theory in the early 1970s. The Ramond (periodic) sector for the world sheet fermions preserved world sheet supersymmetry. In late 1970s, SUSY was found in the stringy spacetime, too. – Luboš Motl Mar 07 '11 at 18:43
  • Only after Ramond's discoveries, supersymmetry was borrowed from Ramond's setup and people tried to write the 4-dimensional supersymmetry algebra as a direct generalization of the 2-dimensional one. The first non-trivial interacting model was the 4D Wess-Zumino model - with a single chiral superfield (one complex boson, one Majorana fermion). It was followed by QFT model buildings - supergravities in the late 1970s and minimal SUSY standard model (MSSM) around 1980. In the early 1980s, it began to be slowly understood that SUGRA should have been extended to the superstring (consistency). – Luboš Motl Mar 07 '11 at 18:46
  • Dear Lubos, I know what causality is, that's why I was asking, because my impression was SUSY predated ST. I suppose I was wrong. – MBN Mar 07 '11 at 19:31
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    Dear Lubos, testing my memory I went to the CERN library and checked for the two words "supersymmetry" and "strings" in any field . The first publication came out at 1985. When checking for supersymmetry, the first publications comes out at 1980. So, us simple experimentalists should be excused not to know all the esoteric history and the way it connected to strings. According to wikipedia it was first found by Hironary Miyazawa in 1966, and rediscovered by others in 1971 concurrent with Ramond. Maybe somebody should edit the supersymmetry article in Wiki. – anna v Mar 07 '11 at 21:35
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    String skeptics are largely not about preventing people from studying string theory. They are against string theorists wildly overstating the evidence for string theory. It is clearly an interesting avenue of research with many potential benefits. Flippantly claiming that it is already proven is absurd. For one thing, SUSY does not imply extra dimensions, which string theory also needs to work. – Zo the Relativist Mar 07 '11 at 22:28
  • You've mentioned this idea about the existence of axions implying a 4d Green-Schwarz mechanism before, and I still don't understand what you're referring to. The use of "4d Green-Schwarz" that I know is when some modulus shifts under an anomalous symmetry, so that its kinetic term must involve the gauge field, effectively generating a Stückelberg mass for the gauge boson. Is this what you're talking about? The axions involved there become longitudinal modes of a gauge boson, so there isn't a physical axionic mode left over.... – Matt Reece Mar 07 '11 at 22:50
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    Dear Anna, most initial work about both SUSY and SUGRA has been done in the 1970s. It's really bad if someone suggests that it was 1980 or even 1985. Never heard of Miyazawa, interesting... – Luboš Motl Mar 08 '11 at 05:52
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    Dear Jerry, if "They are against string theorists wildly overstating the evidence for string theory," then it's OK and they don't really oppose anything because the evidence for the importance of string theory can't be overstated. By the way, SUSY in combination with general relativity implies SUGRA, and SUGRA for consistency actually does require extra dimensions. This can be seen very directly in N=8 SUGRA so you've been misled. There's really no consistent theory of gravity that would manage to deny any insight of string theory. – Luboš Motl Mar 08 '11 at 05:55
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    The proposition that string theory is needed for consistency in any theory respecting postulates of quantum mechanics as well as general relativity is not absurd; it is established science. One may try to protest against the laws of Nature or the laws of mathematics - much like one may protest against the skies' being blue - but at the end, it's Nature and mathematics who decide. – Luboš Motl Mar 08 '11 at 05:58
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    Matt, nope, I am talking - and made it very clear - about the triangle conformal anomaly in N=1 d=4 supergravity which has to cancel and whose cancellation requires a Green-Schwarz mechanism whenever there is at least one linear supermultiplet (with an axion) in the SUGRA content. http://scholar.google.com/scholar?hl=en&q=%22conformal+anomaly%22+supergravity+%22linear+multiplet%22&btnG=Search&as_sdt=0,5&as_ylo=&as_vis=0 – Luboš Motl Mar 08 '11 at 06:01
  • @lubos, there you go overstating your case again. You've even admitted in other threads that it may be possible for some other consistent quantum theory of gravity to be written down, just that you don't believe that it has been written down. And why on earth does SUSY imply that gravity is also supersymmetric? Also, pure supergravity has been shown to be perfectly consistent in d=4. – Zo the Relativist Mar 09 '11 at 16:57
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    No, I surely don't think that one can write down "other" consistent theories of quantum gravity that are not string/M-theory. Where did I write they were possible? SUSY is a symmetry of the laws of physics, so if the symmetry exists, everything has to be supersymmetric. You can't combine apples with oranges, non-SUSY theories with SUSY ones. It makes no sense. Also, it's nonsense that SUGRA only is "perfectly consistent". N=8 SUGRA is perturbatively finite but phenomenologically unacceptable and non-perturbatively inconsistent. Other SUGRAs are as perturbatively non-renormalizable as GR. – Luboš Motl Mar 10 '11 at 21:31
  • Dear @Jerry Schirmer, the reason for "why on earth does SUSY imply that gravity is also supersymmetric?" is very simple. We already know from GR that in the real world the Poincare symmetry cannot be global, it can only be a local one. Furthermore, it is impossible to simultaneously have the supersymmetric extension of the Poincare symmetry being global, while keeping the usual Poincare transformations local. Therefore, super-Poincare symmetry in the real world must be local and local super-Poincare transformations automatically lead to supergravity. – stringpheno Mar 14 '11 at 01:46
  • Discovery of superpartners at the LHC will unambiguously imply some version of N=1 D=4 supergravity coupled to the MSSM. In fact, in a very popular class of models, so-called gauge mediation scenarios, the lightest supersymmetric partner (LSP) is the gravitino - the spin $3/2$ partner of the graviton. – stringpheno Mar 14 '11 at 02:01
  • @Lubos Motl Hi Lubos. Could you please respond to this? I remember you defining this term a couple of times when asked in the comments of your blog, but they aren't Google searchable, so I decided to create something "canonical" any time I forget what "morally true" means. Thanks a bunch. – Uticensis Mar 15 '11 at 19:23
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    Dear @Billare, unfortunately, no, I couldn't respond to it because the page is not found. In general, science can't directly define what is moral. It can only point out relationships between events and properties that people may find moral or immoral. – Luboš Motl Jun 10 '11 at 05:16
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Something analogous happened a couple of decades ago. The discovery of the $W$ and $Z$ bosons simultaneously confirmed the Weinberg/Salam electroweak model and made "how is electroweak symmetry broken?" the key new unanswered question. It's still unanswered, and it's much more challenging, experimentally and theoretically. The discovery of supersymmetry and a Higgs would go a long way toward answering it (the standard scenario in the MSSM is called "radiative electroweak symmetry breaking.")

Analogously, the discovery of superpartners would make the key unanswered question in particle physics "how is supersymmetry broken?" Actually, there are two parts to this question: the first is how the symmetry is broken, and the second is how that breaking is "mediated" to the Standard Model. (This is a somewhat technical story, but the point is that supersymmetry breaking must involve fields beyond just the Standard Model, together with some mechanism that allows the breaking to be felt by the Standard Model.) The question of how the breaking is mediated is likely to be easier to answer than the question of how the breaking itself actually happens.

In any case, though, these will be complicated questions that will depend on the accurate measurement of a number of masses, together with a lot of guesswork and hopefully some luck. There are several good ideas for models, but in the absence of data it's hard to know which ones to believe, and they all have some fairly significant problems.

Matt Reece
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