The Cosmic Landscape

by Leonard Susskind

  Remember that in chapter 2 I explained that an exact twinning of fermions and bosons would cancel the fluctuating energy of the vacuum. Exactly the same is true of the extra, unwanted mass of parti-cles. In a supersymmetric world the violent effects due to quantum fluctuations would be tamed, leaving the particle masses undisturbed. Moreover, even a distorted supersymmetry would alleviate the problem a great deal if the distortion were not too severe. This is the primary reason that elementary-particle physicists hope that supersymmetry is “just around the corner.” It should be noted, however, that distorted supersymmetry cannot account for the absurdly small value of the cosmological constant. It’s just too small.

  The problem of the Higgs mass is similar to the problem of vacuum energy in another way. Just as Weinberg showed that life could not exist in a world with too much vacuum energy, heavier elementary particles would also be disastrous. Perhaps the explanation of the Higgs mass problem lies not in supersymmetry but rather in the enormous diversity of the Landscape and the anthropic need for the mass to be small. In a few years we may know whether supersymmetry really is just around the corner or if it is a mirage that keeps receding as we approach it.

  One question that seems not to have been asked by theoretical physicists is: “If supersymmetry is such a wonderful, elegant, mathematical symmetry, why isn’t the world supersymmetric? Why don’t we live in the kind of elegant universe that string theorists know and love best?” Could the reason be anthropic?

  The biggest threat to life in an exactly supersymmetric universe doesn’t have to do with cosmology but, rather, with chemistry. In a supersymmetric universe every fermion has a boson partner with exactly the same mass, and therein lies the trouble. The culprits are the superpartners of the electron and the photon. These two particles, called the selectron (ugh!) and the photino, conspire to destroy all ordinary atoms.

  Take a carbon atom. The chemical properties of carbon depend primarily on the valence electrons—the most loosely bound electrons in the outermost orbits. But in a supersymmetric world, an outer electron can emit a photino and turn into a selectron. The massless photino flies off with the speed of light, leaving the selectron to replace the electron in the atom. That’s a big problem: the selectron, being a boson, is not blocked (by the Pauli exclusion principle) from dropping down to lower energy orbits near the nucleus. In a very short time, all the electrons will become selectrons trapped in the innermost orbit. Good-bye to the chemical properties of carbon—and every other molecule needed for life. A supersymmetric world may be very elegant, but it can’t support life—not of our kind, anyway.

  If you go back to the physics archive Web site, you will find two other archives, one called General Relativity and Quantum Cosmology, the other Astrophysics. In these archives supersymmetry plays a much less prominent role. Why should a cosmologist pay any attention to supersymmetry if the world is not supersymmetric? To paraphrase Bill Clinton, “It’s the Landscape, stupid.” Although a particular symmetry may be broken to a greater or lesser degree in our little home valley, that doesn’t mean that the symmetry is broken in all corners of the Landscape. Indeed, the portion of the String Theory Landscape that we know most about is the region where supersymmetry is exact and unbroken. Called the supersymmetric moduli space (or supermoduli space), it is the portion of the Landscape where every fermion has its boson and every boson has its fermion. As a consequence, the vacuum energy is exactly zero everywhere on the supermoduli space. Topographically, that makes it a plain at exactly zero altitude. Most of what we know about String Theory comes from our thirty-five-year exploration of this plain. Of course this also implies that some pockets of the megaverse will be supersymmetric. But there are no superstring theorists to enjoy it.

  The Magical Mystery aMazing M-Theory

  By 1985 String Theory—now called superString Theory—had five distinct versions.4 They differed in a number of ways. Two had open strings (strings with two ends) as well as closed strings—three did not. The names of the five are not particularly enlightening, but here they are. The two with open strings are called Type Ia and Ib String Theories. The remaining three with only closed strings are known as Type IIa, Type IIb, and Heterotic String Theories. The distinctions are too technical to describe without boring the reader. But one thing that they have in common is far more interesting than any of the differences: although some have open strings and some don’t, all five versions have closed strings.

  To appreciate why this is so interesting, we need to understand a very disappointing failure of all previous theories. In ordinary theories—theories such as Quantum Electrodynamics or the Standard Model—gravity is an optional “add-on.” You can either ignore gravity or add it into the brew. The recipe is simple: take the Standard Model and add one more particle, the graviton. Let the graviton be massless. Also add some new vertices: any particle can emit a graviton. That’s it. But it doesn’t work very well. The mathematics is intricate and subtle, but at the end of the day, the new Feynman diagrams involving gravitons make hash out of the earlier calculations. Everything comes out infinite. There is no way to make sense of the theory.

  In a way I think it is a good thing that the simple procedure failed. It contains no hint of an explanation of the properties of particles, it has no explanation of why the Standard Model is special, and it explains nothing about the fine-tuning of the cosmological constant or the Higgs mass. Frankly, if it worked, it would be very disappointing.

  But the five String Theories are very clear on this point: they simply cannot be formulated without gravity. Gravity is not an arbitrary input—it is an inevitable outcome. String Theory, in order to be consistent, must include the graviton and the forces that it mediates by exchange. The reason is simple. The graviton is a closed string, the lightest one. Open strings are optional, but closed strings are always there. Suppose we try to create a theory with only open strings. If we succeed we will have a String Theory without gravity. But we will always fail. The two ends of an open string can always find each other and join to form a closed string. Ordinary theories are consistent only if gravity is left out. String Theory is consistent only if it includes gravity. That fact, more than any other, gives string theorists confidence that they are on the right track.

  The four theories labeled Types I and II were first discovered in the 1970s. Each had fatal defects, not in their internal mathematical consistency, but in the detailed comparison with experimental facts about particles. Each described a possible world. They just did not describe our world. Thus, enormous excitement ensued when the fifth version was discovered in Princeton, in 1985. The Heterotic String Theory appeared to be the string theorist’s dream. It looked enough like the real world to perhaps be the real thing. Success was declared imminent.

  Even then there were reasons to be suspicious of the strong claims. For one thing, there was still the problem of too many dimensions: nine of space and one of time. But theorists already knew what to do with the extra six dimensions: “Compactify!” they said. But there are millions of possible choices among Calabi Yau spaces. Moreover, every one of them gives a consistent theory. Even worse, once a Calabi Yau manifold was chosen, there were hundreds of moduli associated with its shape and size. These, too, had to be fixed by hand. Furthermore, the known theories were all supersymmetric: in each case the particles came in exactly matched pairs, which we know does not fit our reality.

  Nevertheless, string theorists were so blinded by the myth of uniqueness that throughout the 1980s and early 1990s they continued to claim that there were only five String Theories. In their imagination the Landscape was very sparse: it had only five points! This of course was nonsense, since each compactification came with many moduli that could be varied; but still, physicists clung to the fiction that there were only five theories to sort through. Even if there were only five possibilities, what principle picked, from among them, the one that describes the real world? No ideas surfaced. But in 1995 came a breakthrough, not in finding
the right version to describe the world, but in understanding the connections among the various versions.

  University of Southern California, 1995

  Every year in late spring or early summer, the world’s string theorists convene for their annual jamboree. Americans, Europeans, Japanese, Koreans, Indians, Pakistanis, Israelis, Latin Americans, Chinese, Muslims, Jews, Christians, Hindus; believers and atheists: we all meet for a week to hear one another’s latest thoughts. Almost all of the four or five hundred participants know one another. The senior people are generally old friends. When we meet we do what physicists always do: give and listen to lectures on the latest hot topics. And have a banquet.

  The year 1995 was memorable, at least to me, for two reasons. First, I was the after-dinner speaker at the banquet. The second reason was an event of momentous importance to the people assembled there: Ed Witten gave a lecture reporting spectacular progress that turned the field in totally new directions. Unfortunately Witten’s lecture went right past me, not because I couldn’t get there, but because I was happily daydreaming about what I would say in the after-dinner speech.

  What I wanted to talk about that evening was an outrageous hypothesis: a guess about how today’s physics might have been discovered by very smart theorists even if physics had been deprived of any experiment after the end of the nineteenth century. The purpose was partly to amuse but also to bring some perspective to what we (string theorists) were attempting. I will come back to it in chapter 9.

  What my daydreaming caused me to miss was a new idea that would become central to my conception of the Landscape. Ed Witten, not just a great mathematical physicist but also a leading figure among pure mathematicians, had long been the driving force behind the mathematical development of String Theory. He is a professor (some would say “The Professor”) and leading light at the intellectually supercharged Institute for Advanced Study. More than anyone, Witten has single-mindedly driven the field forward.

  By 1995 it was becoming clear that the vacuum described by String Theory was far from unique. There were many versions of the theory, each one leading to different Laws of Physics. This was not seen as a good thing but rather as an embarrassment. After all, ten years earlier, the Princeton string theorists had promised not only that the theory was almost unique but also that they were about to find the one true version that describes nature. Witten’s primary objective had been to prove that all but one version was mathematically inconsistent. But instead he found a Landscape, or more accurately, the portion of the Landscape at zero altitude, i.e., the supersymmetric part of the Landscape. Here’s what happened:

  Imagine that physicists had discovered two theories of electrons and photons: the usual Quantum Electrodynamics but also a second theory. In the second theory electrons and positrons, instead of moving freely through three-dimensional space, could move only in one direction, let’s say the x-direction. They were simply unable to move in any other direction. Photons, on the other hand, move in the usual way. The second theory was an embarrassment. As far as physicists could tell, it was mathematically every bit as consistent as the Quantum Electrodynamics that ruled the real world of atoms and photons, but it had no place in their view of the real world. How could there be two theories, equally consistent, with no way to explain why one should be discarded while the other describes nature? They hoped and prayed that someone would discover a flaw, a mathematical contradiction, that would eliminate the unwanted theory and give them reason to believe the world is the way it is because no other world is possible.

  Then, while attempting to prove that the second theory was inconsistent, they hit upon some interesting facts. Not only did they find no inconsistency, but they also began to understand that the two theories were both part of the same theory. The second version, they realized, was merely a limiting version of the usual theory in a region of space with an enormously large magnetic field—a super MRI machine. As any physicist will tell you, a very strong magnetic field will constrain charged particles to move in only one direction: along the magnetic lines of force. But the motion of an uncharged particle, like the photon, is unaffected by the field.5 In other words, there is only one theory, one set of equations, but two solutions. Even better, by varying the magnetic field continuously, a whole family of theories interpolates between the two extremes. The fictitious physicists had discovered a continuous Landscape and set about to explore it. Of course they still had no idea what mechanism might choose among the continuum of solutions—why the world of reality has no background magnetic field. They hoped to explain that later.

  This is exactly the situation that Witten left us with after his 1995 talk in Los Angeles. He had discovered that all five versions of String Theory were really solutions to a single theory: not many theories, but many solutions. In fact they all belonged to a family that includes one more member, a theory that Witten called M-theory. Moreover, the six theories each correspond to some extreme value of the moduli: some distant limiting corner of the Landscape. As in the example of the magnetic field, the moduli could be continuously varied so that one theory morphed into any of the others! “One theory—many solutions”: that became the guiding slogan.

  There are many conjectures about what M stood for. Here are some of the possibilities: mother, miracle, membrane, magic, mysterious, and master. Later, matrix was added. No one seems to know for sure what Witten had in mind when he coined the term M-theory. Unlike the previously known five theories, the new cousin is not a theory with nine space dimensions and one time. Instead, it is a theory with ten dimensions of space and one of time. Even more alarming, M-theory is not a theory of strings: the basic objects of M-theory are membranes, two-dimensional sheets of energy that resemble elastic sheets of rubber instead of one-dimensional rubber bands. The good news was that M-theory seemed to provide a unifying framework in which the various String Theories appear when one or more of the ten dimensions of space are rolled up by compactification. This was real progress that held the promise of a unifying foundation for String Theory. But there was also a down side. Almost nothing was known about the mix of eleven-dimensional general relativity with quantum mechanics. The mathematics of membranes is horribly complicated, far beyond that of strings. M-theory was as dark and mysterious as any quantum theory of gravity had ever been before String Theory made its appearance. It seemed as if we had taken one step forward and two steps backward.

  It didn’t stay that way for long. By the next string meeting, in the summer of 1996, I had the pleasure of reporting that three of my friends and I had uncovered the secret of M-theory. We had found the underlying objects of the theory, and the equations governing them were incredibly simple. Tom Banks, Willy Fischler, Steve Shenker, and I discovered that the fundamental entities of M-theory were not membranes but simpler objects, basic “partons” of a new kind. In some ways similar to Feynman’s old partons, these new constituents had an astonishing ability to assemble themselves into all kinds of objects. The graviton itself, once thought to be the most fundamental particle, was a composite of many partons. Assemble the same partons in a different pattern, and membranes emerged. In another pattern they formed a black hole. The detailed equations of the theory were far simpler than the equations of String Theory, simpler even than the equations of general relativity. The new theory is called Matrix Theory or sometimes M(atrix) Theory to emphasize its connection to M-theory.

  Witten was not the first to speculate about a connection between an eleven-dimensional theory and String Theory. For years a number of physicists had tried to call attention to an eleven-dimensional theory with membranes in it. Mike Duff at Texas A&M (now of Imperial College, London) had had most of the ideas years earlier, but string theorists weren’t buying it. Membranes were just too complicated, the mathematics too poorly understood, for Duff’s seminal idea to be taken seriously. But Witten being Witten, string theorists latched on to M-theory and never let go.

  What is it about M-theory that so captured the ima
gination of theoretical physicists? It is not a String Theory. No one-dimensional filaments of energy inhabit this world of eleven space-time dimensions. So why, all of a sudden, did string theorists become interested in two-dimensional sheets of energy—membranes, as they are called? The answers to these riddles lie in the subtle mysteries of compactification.

  Let’s return to the infinite cylinder and recall how we got to it. Beginning with an infinite sheet of paper, we first cut out an infinite strip a few inches wide. Think of the two edges as the ceiling and floor of a two-dimensional room. The room is extremely big. It goes on forever in the x-direction, but in the y-direction it is bounded above and below by the floor and ceiling. In the next step the ceiling is joined to the floor to make a cylinder.

  Imagine a particle moving through the infinite room. At some point it may arrive at the ceiling. What happens next? If the strip were rolled up into a cylinder, there would be no problem: the particle would just keep going, passing through the ceiling and reappearing at the floor. In fact we don’t really need to bend the paper into a cylinder; it is enough to know that every point on the ceiling is matched to a unique point on the floor so that when the particle passes through an edge it suddenly jumps to the other edge. We can roll it up or leave it flat: we need only to keep track of the rule that each ceiling point is identified with the floor point vertically below it.