Warped Passages (52 page)

Towards the end of the 1990s, many physicists, myself included, expanded their horizons to include the possibility of branes. We asked ourselves, “What if there were a higher-dimensional universe in which the particles and forces we know about don’t travel in all dimensions, but are confined to fewer dimensions on a lower-dimensional brane?”

Brane scenarios introduced many new possibilities for the global nature of spacetime. If Standard Model particles are confined to a brane, then we are as well, since we and the cosmos that surrounds us are composed of these particles. Furthermore, not all particles have to be on the same brane. There might therefore be entirely new and unfamiliar particles that experience different forces and interactions from the ones we know. The particles and forces we observe might be only a small part of a much larger universe. Two physicists from
Cornell, Henry Tye and Zurab Kakushadze, coined the term “brane-worlds” to label such scenarios. Henry told me that he used the term so that he could, in one fell swoop, describe all of the many ways in which the universe could include branes without being wedded to any particular possibility.

Although the proliferation of potential braneworlds might be frustrating to string theorists trying to derive a single theory of the world, it is also thrilling. These are all real possibilities for the world in which we live, and one of them might truly describe it. And because the rules of particle physics would be somewhat different in a higher-dimensional universe than particle physicists have assumed, extra dimensions introduce new ways of trying to address some of the puzzling features of the Standard Model. Although these ideas are speculative, braneworlds that address problems in particle physics should soon be testable in collider experiments. This means that experiments, rather than our prejudice, could ultimately decide whether these ideas apply to our world.

We are about to investigate some of these new braneworlds. We’ll ask what they might look like and what their consequences could be. We will not restrict ourselves to braneworlds derived explicitly from string theory, but will consider model braneworlds that have already introduced new ideas into particle physics. Physicists are so far from understanding the implications of string theory that it would be premature to exclude models just because no one has yet found a string theory example with a particular set of particles or forces or a particular distribution of energy. These braneworlds should be thought of as targets for string theory explorations. In fact, the warped hierarchy model I’ll talk about in Chapter 20 was derived from string theory only after Raman Sundrum and I introduced it as a braneworld possibility.

The following chapters will present several different braneworlds. Each of them will illustrate a completely new physical phenomenon. The first will show how braneworlds can evade the anarchic principle; the second will show that dimensions can be much larger than we previously thought; the third will show that spacetime can be so curved that we would expect objects to have very different sizes and masses; and the last two will show that even infinite extra dimensions
can be invisible when spacetime is curved, and that spacetime might even appear to have different dimensions in different places.

I’m presenting several models because they are all real possibilities. But just as important, each of them contains some new feature that physicists recently thought impossible. I’ll summarize the significance of each model and how it violated conventional wisdom at the end of each of the chapters. Feel free to read these bullet summaries first to get the big picture, a quick résumé of the significance of the particular model that chapter explains.

Before proceeding to these braneworlds, I’ll now briefly present the first known braneworld, one which was derived directly from string theory. Petr Hořava and Edward Witten hit upon this braneworld—called “HW” after their initials—in the course of exploring string theory duality. I’m presenting this model because it is interesting in its own right, but also because it has several properties that foreshadow features of the other braneworlds we will soon encounter.

Hořava-Witten Theory

The HW braneworld is pictured in Figure 72. It’s an eleven-dimensional world bounding two parallel branes, each of which has nine spatial dimensions bounding a bulk space that has ten spatial dimensions (eleven of spacetime). The HW universe was the original braneworld theory; in HW, each of the two branes contains a different set of particles and forces.

The forces on the two branes are the same as those of the heterotic string that was introduced in Chapter 14; that was the theory that David Gross, Jeff Harvey, Emil Martinec, and Ryan Rohm discovered, in which oscillations moving to the left or the right along the string interact differently. Half of those forces are confined to one of the two boundary branes, and the other half are confined to the other. There are enough forces and particles confined to each of the two branes that either one of them could conceivably contain all the particles of the Standard Model (and therefore us). Hořava and Witten assumed that the particles and forces of the Standard Model reside on
one of the two branes, whereas gravity and other particles that are part of the theory, but which we haven’t observed in our world, are free to travel on the other brane or off the branes in the full eleven-dimensional bulk.

Figure 72.
Schematic drawing of the Hořava-Witten braneworld. Two branes with nine spatial dimensions (represented schematically by two-dimensional branes) are separated along the eleventh spacetime dimension (the tenth spatial dimension). The bulk includes all spatial dimensions: those nine that extend in the spatial directions along the two branes, and the additional one that extends between them.

In fact, the HW braneworld didn’t just have the same forces as the heterotic string—it
was
the heterotic string, albeit with strong string coupling. This is another example of duality. In this case, an eleven-dimensional theory with two branes bounding the eleventh dimension (the tenth dimension of space) is dual to the ten-dimensional heterotic string. That is to say, when the interactions of the heterotic string are very strong, the theory is best described as an eleven-dimensional theory with two boundary branes and nine spatial dimensions. This is not unlike the duality between ten-dimensional superstring theory and eleven-dimensional supergravity that was discussed in the previous chapter. But in our present example, the eleventh dimension is not rolled up, but is instead bounded between two branes. Once again, an eleven-dimensional theory can be equivalent to a ten-dimensional one, albeit when one theory has strong interactions and the other has feeble ones.

Of course, even if Standard Model particles are confined to a brane, the theory would still have more dimensions than we see around us. If the Hořava-Witten braneworld is to correspond to reality, six of its dimensions must be unseen. Hořava and Witten assumed that six dimensions were curled up into a tiny Calabi-Yau shape.

Once six dimensions are curled up, you can think of the HW universe as a five-dimensional effective theory with four-dimensional boundary branes. This picture of a five-dimensional universe with two boundary branes is an interesting one that many physicists have investigated. Raman and I applied some of the techniques that two physicists, Burt Ovrut and Dan Waldram, used to study the HW effective theory to the different five-dimensional theories that I’ll discuss in Chapters 20 and 22.

One fascinating element of the Hořava-Witten braneworld is that it can accommodate not only the Standard Model particle and forces, but also a full Grand Unified Theory. And because gravity originates in higher dimensions, it’s possible for gravity and other forces to have the same strength at high energy in this model.

The HW braneworld illustrates three reasons why braneworlds can matter for real-world physics. First, it involves more than a single brane. This means that it can contain forces and particles that interact with each other only weakly because of the distance between the two branes on which they are bound. The only way that particles confined to different branes can communicate is through common interactions with bulk particles. This first feature will be significant in the sequestering models that we’ll look at in the next chapter.

The second important braneworld feature is that any braneworld introduces new length scales into physics. These new scales, like the size of the additional dimensions, might be relevant to unification or the hierarchy problem. Problems in both of these theories center around why there should be very different energy and mass scales in a single theory, and why quantum effects don’t tend to equate the two.

Finally, branes and the bulk can carry energy. This energy can be stored by the branes and by the higher-dimensional bulk; it doesn’t depend on the particles that are present. Like all forms of energy, it curves the bulk spacetime. We will soon see that such curvature of
spacetime caused by energy spreading throughout the space can be very important to braneworlds.

The HW braneworld certainly has many tantalizing features. But it also suffers from the problems all realizations of string theory seem to have in reproducing known physics. Hořava-Witten theory is very difficult to test experimentally because its dimensions are so small. The many unseen particles have to be heavy enough to have avoided detection, and six of its dimensions have to be curled up, even though neither the size nor the shape of the curled-up dimensions has been determined.

Proceeding along these lines, one might accidentally hit on the version of string theory that correctly describes nature; this possibility is not definitively ruled out. For this to happen, we would have to be very lucky indeed. But problems in particle physics also beckon, and it is worth investigating how these problems might be resolved in a world with extra dimensions of space and branes that extend along only a restricted subset of these dimensions. That is what the rest of this book is about.

What to Remember

• Braneworlds are possible within the framework of string theory. Particles and forces in string theory can be trapped on branes.
  
• Gravity is different from other forces. It is never confined to a brane and always spreads through all dimensions.
  
• If string theory describes the universe, it could contain many branes. Braneworlds are very natural in this context.
  

17

Sparsely Populated Passages: Multiverses and Sequestering

Just turn around now

(’cause) you’re not welcome anymore.

Gloria Gaynor

Despite its explicit prohibition on the Heavenbrane, Icarus III ultimately returned to gambling. After ignoring repeated reprimands, he was sentenced to confinement on the Jailbrane, a distant brane separated from the Heavenbrane along a fifth dimension. Even after he was sequestered on the Jailbrane, Ike doggedly tried to contact his former buddies. But the distance between their two branes made communication difficult. He was reduced to flagging down passing bulk mail carriers, many of whom ignored his entreaties altogether. The few who did stop always conveyed his messages to the Heavenbrane, but at a frustratingly leisurely pace.

Meanwhile, back on the Heavenbrane, disaster loomed. The guardian angels, who had so bravely rescued the hierarchy, had no respect for the other residents’ family values and were on the verge of creating intergenerational instability. Heaven’s fallen angels considered all pairings acceptable and encouraged everyone to mix with a trophy partner from another generation.

When Ike learned of the threat, he was aghast and he resolved to redeem the situation. Ike realized that by using the slow and deliberate manner with which he was constrained to communicate with the Heavenbrane, he could judiciously feed the massive egos of the unruly angels living there. Thanks to Ike’s helpful intervention, the angels stopped threatening the social order. Although Icarus III still had to serve his sentence, the relieved residents on the Heavenbrane honored him forevermore in urban myth.

This chapter is about
sequestering
, one of several reasons that extra dimensions could prove to be important for particle physics. Sequestered particles are physically separated on different branes. By confining different particles to different environments, sequestering might explain the distinctive properties that distinguish one particle from another. Sequestering might also be the reason that the anarchic principle, which says that everything should interact, doesn’t always hold true. If particles are separated in extra dimensions, they are less likely to interact with one another.

In principle, particles could have been sequestered in three spatial dimensions. But as far as we can tell, all directions and all places in three-dimensional space are the same. The known laws of physics tell us that any particle can be anywhere in the three dimensions we see, so sequestering in three dimensions isn’t an option. However, in higher-dimensional space, photons and charged objects cannot necessarily be just anywhere. Extra dimensions introduce a way to separate particles. Distinct particle types might be restricted to separate regions of space occupied by different branes. Because not all points in extra dimensions look the same, extra dimensions introduce a way to separate particles by confining different particle types to separated branes.