Warped Passages (53 page)
Theories that sequester particles have the potential to solve many problems. The story about Ike refers to my first foray into extra dimensions—the application of sequestering to supersymmetry breaking. Whereas four-dimensional theories face serious problems because supersymmetry-breaking models generally introduce unwanted interactions, sequestered supersymmetry-breaking models appear to be far more promising. Sequestering might also explain why particles have different masses from one another, and why proton decay does not occur in extra-dimensional models. In this chapter, we’ll explore sequestering and a few of its particle physics applications. We’ll see how even ideas, such as supersymmetry, that we thought applied to four-dimensional spacetime might be more successful in an extra-dimensional context.
My Passage to Extra Dimensions
We physicists are fortunate to have many conference opportunities to meet and share stimulating research ideas with colleagues. But such an overwhelming number of conferences and workshops in particle physics are held each year that choosing which invitations to accept can be difficult. Some are major gatherings that provide an opportunity to hear about others’ recent work and to share your latest results. Some are relatively short conferences, lasting two or three days, in which physicists report major new results in a highly specialized field. Other meetings are longer workshops where physicists begin or complete collaborations with colleagues. Sometimes conferences are held in such spectacular locations they are just too good to miss.
Although Oxford is a very nice place, the supersymmetry conference that I attended there in early July of 1998 fits best into the first category. Supersymmetry, which for many years was considered the only possible way out of the hierarchy problem, has evolved over time into a major research area, and every year physicists gather to discuss recent progress in the field.
The Oxford conference held a surprise, however. The most interesting topic was not supersymmetry, but the newly emergent idea of extra dimensions. One of the most stimulating talks was about large extra dimensions, the subject of Chapter 19. Other talks were on the fate of string theory’s extra dimensions, and still others discussed potential experimental implications of extra dimensions. The novelty and speculative nature of such ideas was clear from the title of Chicago theorist Jeff Harvey’s talk: he and several later speakers jokingly named their talks after
Fantasy Island
. Joe Lykken, a theorist from Fermilab, even had a slide with a little man pointing to “Da brane. Da brane.” (Needless to say, the joke about Tattoo, famous for welcoming “da plane” to Fantasy Island, was lost on those who had not experienced the joys of American seventies TV.)
Despite the jokes, I returned from the Oxford supersymmetry conference thinking about extra dimensions and why problems in particle physics might be solved in an extra-dimensional world. Although I
was skeptical about the large extra dimensions that was one of the hot topics, and did not plan to work on them myself, I was fairly convinced that branes and extra dimensions could be important model building tools with the potential to explain some of the mysterious particle physics phenomena that have defied simple four-dimensional explanations.
That year I was planning to spend the rest of the summer in Boston. This was not the norm for me at the time; most of the Boston theoretical physics community, myself included, travel for a large part of each summer, attending assorted conferences and workshops. But I had decided to stay at home to relax and think about new ideas.
Raman Sundrum, who was then a postdoctoral fellow at Boston University, had also decided to remain in Boston that summer. I had often met Raman at conferences or when we visited each other’s institutions, and we had even briefly overlapped as postdoctoral fellows at Harvard. Since Raman had already thought about extra dimensions, I decided that it could be useful to discuss my ideas and questions with him.
Raman is an interesting character. Whereas most physicists in the early stages of their career work on relatively safe problems—questions of general interest in which they are likely to make progress—Raman insisted on focusing on whatever he considered most important, even when it was an extremely difficult problem or diverged considerably from other people’s interests. Despite his obvious talent, his idiosyncratic approach had kept him from a faculty job and brought him to his third postdoctoral position. But at that time, Raman was thinking about extra dimensions and branes; his interests and those of the rest of the physics community had begun to converge.
Our collaboration began at MIT’s branch of Toscanini’s (now sadly closed), an ice cream shop in the MIT student center that served great ice cream and very good coffee. Toscanini’s was the ideal venue for discussing ideas without constraints or interruptions, as well as indulging in the delicious research stimulants that were available there.
From those early days, chatting over coffee, our research evolved and jelled as the summer progressed. By August it had reached the
point where we needed bigger and bigger blackboards to hold all the details we were discussing. Since the blackboard in my office at MIT, where I was then a professor, was rather small, we would wander the “infinite corridor” (the very long hallway that runs the length of MIT’s main building) searching for empty classrooms.
The particular research problem we focused on was the application of sequestering to supersymmetry breaking. The idea was to sequester particles responsible for supersymmetry breaking from the Standard Model particles and thereby prevent unwanted interactions between them (see Figure 73). We chose the word “sequester” to distinguish models in which particles are separated on different branes from the so-called “hidden sector” models of supersymmetry breaking that were fashionable at the time. In hidden sector models, supersymmetry-breaking particles interacted feebly with Standard Model particles,
but weren’t actually hidden (despite the name), and therefore could interact in ways that are not acceptable in the real world.
Figure 73.
In this model for supersymmetry breaking, there are two branes. Standard Model particles are on one brane, and particles that break supersymmetry are sequestered on the other. The two branes each have three spatial dimensions and are separated in a fifth spacetime dimension, which is the fourth dimension of space.
In the beginning I was very enthusiastic about our ideas and Raman was skeptical, although our roles alternated over time. But with one enthusiast and one skeptic, we quickly covered a lot of ground and got to the heart of the physics we were thinking about. Sometimes we even dismissed ideas too quickly, but usually one or the other of us maintained a point of view long enough to make progress.
Francis Bacon, who along with Galileo is considered one of the founders of the modern scientific method, described the difficulty of making progress while nonetheless retaining the skepticism necessary to ensure the correctness of your results.
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How can you take an idea seriously enough to delve into its consequences, while simultaneously suspecting that it might be incorrect? Given enough time, a single person can fluctuate between these two attitudes and arrive at the correct answer. But with two of us taking opposing attitudes, it was often a matter of hours or even minutes before we discarded an intriguing but faulty idea.
Nonetheless, the idea we started with, sequestering to prevent unwanted interactions in supersymmetric theories, seemed to me as if it had to be right. Nothing in four dimensions worked in a sufficiently compelling way, and extra dimensions seemed to have all the necessary ingredients for a successful model. However, it was not until the end of the summer that Raman and I understood sequestering and its consequences for supersymmetry breaking well enough to finally see eye to eye and converge on its merits.
Naturalness and Sequestering
The reason that sequestering could be important is that it is a way to prevent the problems caused by the anarchic principle, the unofficial rule that says that in four-dimensional quantum field theory, anything that can happen will happen. The problem with the anarchic principle
is that theories end up predicting interactions and relationships among masses that are not seen in nature. Even interactions that don’t occur in a classical theory (the one without quantum mechanics taken into account) will occur once virtual particles are included; virtual particle interactions induce all possible interactions.
Here’s an analogy that illustrates why. Suppose you told Athena that it would snow tomorrow, and Athena then told Ike. Even though you had no direct communication with Ike, your communication would nonetheless influence what Ike would wear the next day—he would put on a parka because of your virtual advice.
Similarly, if a particle interacts with a virtual particle, and that virtual particle interacts in turn with a third particle, the net effect is that the first and the third particles interact. The anarchic principle tells us that processes involving virtual particles are bound to occur, even if they don’t happen classically. And those processes often induce unwanted interactions.
Many of the problems in particle physics theories stem from the anarchic principle. For example, the quantum contributions to the Higgs particle’s mass that result from virtual particles are the root of the hierarchy problem. Any path that the Higgs particle takes can be temporarily interrupted by heavy particles, and these interventions increase the Higgs particle’s mass.
We saw another example involving the anarchic principle in Chapter 11. In most theories with broken supersymmetry, virtual particles induce unwanted interactions—interactions that we know from experiments do not take place. Those interactions would change the identity of the known quarks and leptons. Such
flavor-changing interactions
either don’t occur in nature or occur very rarely. If we want a theory to work, we must somehow eliminate these interactions—which the anarchic principle tells us will arise.
Virtual particles don’t necessarily lead to these unwanted predictions. The theory won’t predict these unwanted interactions in the unlikely event that there are enormous cancellations between the classical and quantum mechanical contributions to a physical quantity. Even though the classical and quantum contributions would individually be much too big, the two together could conceivably add up to an acceptable prediction. But this way of getting around the
problem is almost certainly a stopgap measure substituting for a true solution. None of us really believe that such precise, accidental cancellations are the fundamental explanation for the absence of certain interactions. We grudgingly employ the fortuitous cancellations as a crutch so that we can ignore these problems and proceed to investigate other aspects of our theories.
Physicists believe that interactions are absent from a theory only if the interactions were eliminated in a way that fits the physicists’ notion of what’s natural. In the everyday world, the word “natural” refers to things that happen spontaneously, without human intervention. But for particle physicists, “natural” means more than something that happens—it means something that, if it should happen, would not present a puzzle. For physicists, it is only “natural” to expect the expected.
The anarchic principle and the many undesirable interactions that quantum mechanics will induce tell us that some new concepts must enter into any model of physics that underlies the Standard Model if this model is to have a chance of being correct. One reason that symmetries are so important is that they are the only natural way in a four-dimensional world to guarantee that unwanted interactions do not occur. Symmetries essentially provide an extra rule about which interactions can conceivably happen. You can readily understand this phenomenon with the help of an analogy.
Suppose that you prepare six table settings, but you have to prepare them so that all six settings are the same. That is, your settings permit a symmetry transformation that interchanges every pair of settings. Without such a symmetry, you could in principle have given one person two forks, another three, and someone else a pair of chopsticks. But with the symmetry constraints, you can only make settings in which all six people have the same number of forks, knives, spoons, and chopsticks—you could never give one person two knives and another person three.
Similarly, symmetries tell you that not all interactions can occur. Even if many of the particles interact, quantum contributions generally won’t produce interactions that violate a symmetry if the classical interactions preserve that symmetry. If you don’t start with symmetry-violating interactions, you won’t ever generate any (aside from the
rare known anomalies mentioned in Chapter 14), even when you include all possible interactions involving virtual particles. By imposing symmetry on your table settings, you will always end up with identical settings, no matter how many changes you make, such as adding grapefruit spoons or steak knives. Similarly, interactions that are inconsistent with a symmetry will not be induced, even when quantum mechanical effects are taken into account. If a symmetry weren’t already violated in the classical theory, there would be no path that a particle could take that could induce a symmetry-violating interaction.
