Warped Passages (51 page)

Finding a unique Standard Model candidate looked like it would be as hard as ever. String theorists’ euphoria about duality was tempered by this realization. However, those of us who were looking for new insights into observable physics were in heaven. With the new possibilities for forces and particles confined to branes, it was time for us to rethink the starting point for particle physics.

The feature of branes that is essential to their potentially observable applications is that they can trap particles and forces. The purpose of this chapter is to give you a flavor of how this works. We’ll begin by explaining why the branes of string theory confine particles and forces. We’ll consider the braneworld idea and the first known braneworld, one which was derived from duality and string theory. In the chapters that follow, we’ll proceed to those aspects of braneworlds and their potential physical applications that I find most exciting.

Particles and Strings and Branes

As Ruth Gregory, a general relativist from Durham University, puts it, branes in string theory come “fully loaded” with particles and forces. That is, certain branes always have particles and forces that are trapped on them. Like housebound cats that never venture beyond the walls of their domicile, those particles that are confined to branes never venture off them. They can’t. Their existence is predicated on the presence of the branes. When they move, they move only along the spatial dimensions of the brane; and when they interact, they interact only on the spatial dimensions spanned by the brane. From the perspective of brane-bound particles, if it weren’t for gravity or bulk particles with which they might interact, the world might as well have only the dimensions of the brane.

Let’s now see how string theory can confine particles and forces on branes. Imagine that there is only one D-brane, suspended somewhere in a higher-dimensional universe. Because, by definition, both ends of an open string must be on a single D-brane, this D-brane would be where all open strings begin and end. The ends of each open string wouldn’t be stuck in any particular location, but they would have to lie somewhere on the brane. Like train tracks that confine wheels but allow them to roll, the branes act as fixed surfaces in which the ends of the string are confined but can nonetheless move.

Because the vibrational modes of open strings are particles, the modes of an open string with both ends confined to a brane are particles that are confined to this brane. Those particles would travel in and interact only along the dimensions spanned by the brane.

It turns out that one of these particles arising from a brane-bound string is a gauge boson that can communicate a force. We know this because it has the spin of a gauge boson (which is 1), and because it interacts just as a gauge boson should. Such a brane-bound gauge boson would communicate a force that would act on other brane-bound particles, and calculations show that the particles on the receiving end are always charged under this force. In fact, the endpoint of any string ending on the brane would act like a charged particle. The presence of the brane-bound force and these charged particles is what
tells us that a D-brane of string theory comes “loaded” with charged particles and a force that acts upon them.

In setups with more than one brane, there will be more forces and more charged particles. Suppose, for example, that there were two branes. In that case, in addition to the particles confined to each of the branes, there would be a new type of particle arising from strings whose two ends were on the two different branes (see Figure 70).

Figure 70.
A string that begins and ends on a single brane can give rise to a gauge boson. A string with each end on a different brane gives rise to a new type of gauge boson. When the branes are separated, the gauge boson has nonzero mass.

It turns out that if the two branes are separated from each other in space, the particles associated with the string that extends between them will be heavy. The mass of the particles arising from the vibrational modes of this string grows with the distance between the branes. This mass is like the energy that gets stored when you stretch a spring—the more it is stretched, the more energy it contains. Similarly, the lightest particle that arises from a string stretched between two branes will have a mass that increases in proportion to the brane separation.

However, when a spring is relaxed in its rest position, it doesn’t store any energy. Similarly, if the two branes are not separated—that is, if they are in the same place—the lightest string particle arising from the string with an end on each brane is massless.

Let’s now assume that the two branes coincide, so that they produce some massless particles. One of these massless particles would be a gauge boson—not one of the gauge bosons that arises from strings with both ends on a single brane, but a distinct, new one. This new
massless gauge boson, which arises only when there are coincident branes, communicates a force that acts on particles on either one or both of the two branes. Furthermore, as with all other forces, the forces on the brane are associated with a symmetry. In this case the symmetry transformation would be the one that exchanges the two branes (which a punning Igor might enjoy).
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Of course, if two branes really were in the same place, you might think it a little odd to refer to them as two distinct objects. And you would be right: if two branes are in the same place, you can just as well imagine them as a single brane. This new brane exists in string theory. It is secretly two coincident branes, and has the properties those branes would have. It houses all the different types of particles discussed above: the particles that arise from open strings ending on each brane in the original two-brane description, as well as the strings whose ends are both on a single brane.

Now imagine that many branes are superimposed. There would then be many new types of open string because the two string ends can be confined to any of the branes (see Figure 71). Open strings that extend between different branes, or the strings that begin or end on any single one of the branes, imply new particles, composed of the vibrational modes of these strings. Once again, these new particles include new types of gauge boson and new types of charged particle. And once again the new forces are associated with new symmetries that interchange the various superimposed branes.

Figure 71.
Each string that begins and ends on the same brane or that extends between branes gives rise to gauge bosons. When the branes coincide, there are new massless gauge bosons, corresponding to each of the ways in which a string can begin and end on each of the coincident branes.

So indeed, branes come “loaded” with forces and particles; many branes mean rich possibilities. Furthermore, even more intricate
situations can arise involving separated batches of branes. Branes situated in different places would carry entirely independent particles and forces. The particles and forces that are confined to one group of branes would be entirely different from the particles and forces confined to the others.

For example, if the particles of which we are composed, together with electromagnetism, are all confined to one brane, we would experience the electromagnetic force. However, particles that are confined to distant branes would not; those foreign particles would be insensitive to electromagnetism. On the other hand, particles confined to distant branes could experience novel forces to which we are completely insensitive.

An important property of such a setup, which will be relevant later on, is that particles on separated branes don’t interact with each other directly. Interactions are local: they can take place only among particles in the same place; particles on separated branes would be too far apart to interact with each other directly.

You might compare the bulk, the full higher-dimensional space, to a huge tennis stadium with separate matches going on throughout. The ball on any one court would go back and forth across the net and could move anywhere on that court. However, each match would proceed independently of the others, and each ball would stay on its own isolated court. Just as the ball in a given court should stay there and only the two tennis players on that court would have access to it, brane-confined gauge bosons or other brane-confined particles interact only with objects on their own brane.

However, particles on separate branes can communicate with one another if there are particles and forces that are free to travel throughout the bulk. Such bulk particles would be free to enter and leave a brane. They might occasionally interact with particles on a brane, but they can also travel freely in the full higher-dimensional space.

A setup with separated branes and bulk particles that communicate between them would be like a stadium with separate simultaneous matches in which the players in the separate games have the same coach. The coach, who might well want to keep an eye on several games going on at the same time, would travel from one court to another. If one player wanted to communicate something to a player
on another court, he could tell the coach who could carry the message over. The players wouldn’t communicate directly during their matches, but they could nonetheless communicate via a person who travels between their respective courts. Similarly, bulk particles could interact with particles on one brane and subsequently interact with particles on a distant brane, thereby permitting the particles that are confined to separated branes to communicate indirectly.

In the next section we will see that the graviton, the particle that communicates the gravitational force, is one such bulk particle. In a higher-dimensional setup, it would travel throughout the higher-dimensional space and interact with all particles everywhere, whether they are on a brane or not.

Gravity: Different Again

Gravity, unlike all other forces, is never confined to a brane. Brane-bound gauge bosons and fermions are the result of open strings, but in string theory, the graviton—the particle that communicates gravity—is a mode of a closed string. Closed strings have no ends, and therefore there are no ends to pin down on a brane.

Particles that are the vibrational modes of closed strings have unrestricted license to travel in the full higher-dimensional bulk. Gravity, the force we know to be communicated by a closed-string particle, is thus once again singled out from the other forces. The graviton, unlike gauge bosons or fermions,
must
travel though the entire higher-dimensional spacetime. There is no way to confine gravity to lower dimensions. In later chapters we will see that, amazingly, gravity can be localized near a brane. But one can never truly confine gravity on a brane.

This means that although braneworlds could trap most particles and forces on branes, they will never confine gravity. This is a nice property. It tells us that braneworlds will always involve higher-dimensional physics, even if the entire Standard Model is stuck on a four-dimensional brane. If there is a braneworld, everything on it will still interact with gravity, and gravity will be experienced everywhere in the full higher-dimensional space. We’ll soon see why
this important distinction between gravity and other forces might help to explain why gravity is so much weaker than the other known forces.

Model Braneworlds

Very soon after physicists recognized the importance of branes to string theory, branes became the focus of intense study. In particular, physicists were eager to learn about their potential relevance to particle physics and our conception of the universe. As of now, string theory doesn’t tell us whether branes exist in the universe and, if they do, how many there are. We know only that branes are an essential theoretical piece of string theory, without which it wouldn’t fit together. But now that we know that branes are part of string theory, we have also begun to ask whether they could be present in the real world. And if they are, what are the consequences?

The potential existence of branes opens up many new possibilities for the composition of the universe, some of which might even be relevant to the physical properties of matter that we observe. The string theorist Amanda Peet, upon hearing Ruth Gregory’s expression “fully loaded” branes, interjected that branes “blasted open the field of string-based model building.” After 1995, branes became a new model building tool.