Warped Passages (48 page)

What to Remember

• The
  graviton
  is the particle that communicates the gravitational force, much as the photon communicates the electromagnetic force.
  
• According to string theory, the fundamental objects of the world are
  strings
  , not pointlike particles.
  
• Later models of extra dimensions won’t explicitly use string theory; at distances greater than the minuscule Planck scale length (10
  ^-33
  cm), particle physics suffices.
  
• Nonetheless, string theory is important to particle physics, even at low energies, because of the new concepts and analytic tools it introduces.
  

15

Supporting Passages: Brane Development

Insane in the membrane

Insane in the brain.

Cypress Hill

Ike Rushmore XLII decided to dive down once again to the minuscule Planck scale. Happily, his souped-up Alicxvr worked perfectly and he smoothly arrived in a ten-dimensional universe filled with strings. Eager to explore his new environment, Ike cranked up the hyperdrive attachment he had just purchased from Gbay. He watched with fascination as strings collided and tangled in mesmerizing ways.

Although Ike worried that the Alicxvr might break down, he was curious to learn more about this novel world. So he increased the pressure on the hyperdrive lever. At first strings collided together even more frequently. But when he cranked up the lever still more, he entered a new, completely unrecognizable environment. Ike couldn’t even tell whether spacetime was intact. But he kept cranking up the hyperdrive, and, strangely enough, emerged unscathed.
²⁶

However, his surroundings were now quite different. Ike was no longer in the ten-dimensional universe he had started off in. He was instead in an eleven-dimensional universe filled with particles and branes. And, odd as it seemed, nothing in this new universe interacted very much. When Ike looked back at his controls, he discovered that the hyperdrive lever had mysteriously been reset to low. Confused and rather exasperated, Ike cranked up the lever once again, only to find himself back where he started. When Ike checked the controls, he discovered the hyperdrive lever was once again back at low.

Ike thought his Alicxvr was probably malfunctioning. But when he checked his up-to-date manual he discovered that his device was operating perfectly—high hyperdrive in ten-dimensional string theory was the same as low hyperdrive in an alternate eleven-dimensional world. And vice versa.

The manual didn’t say what should happen when the hyperdrive wasn’t very low or very high, so Ike entered the spacernet and put himself on the wait-list for an improved version that would solve the problem. But the Alicxvr designers promised only that the release date would be some time within the millennium.

In today’s physics world, you might say that “string theory” is a misnomer. In fact, the theorist Michael Duff facetiously refers to “string theory” as “the theory formerly known as strings.” String theory is no longer just the theory of strings extending in one spatial direction, but also the theory of branes that can extend in two, three, or more dimensions.
²⁷
We now know that branes, which can extend in any number of dimensions up to the number that superstring theory contains, are just as much a part of superstring theory as are strings themselves. Theorists ignored them earlier on because they studied strings when the string interaction strength “lever” was low and brane interactions were less important. Branes turned out to be the missing piece that miraculously completed several jigsaw puzzles.

In this chapter, I’ll describe the evolution of branes from an amusing, neglected curiosity into a central player in the string theory story. We will see several ways in which branes helped to resolve some bewildering aspects of string theory since the mid-1990s. Branes helped physicists to understand the origin of mysterious particles in string theory that couldn’t possibly arise from strings. And when physicists included branes, they discovered
dual theories
—pairs of theories that seem very different from each other but have the same physical consequences. The opening story refers to one remarkable example of duality that this chapter will explore: an equivalence between ten-dimensional superstring theory and eleven-dimensional supergravity, which is a theory that contains branes but no strings.

This chapter will also introduce
M-theory
, an eleven-dimensional theory that embraces both superstring theory and eleven-dimensional
supergravity, and whose existence was inferred using the insights from branes. No one really knows what the “M” stands for—the term’s originator, Edward Witten, deliberately left it ambiguous—but suggestions have included “membrane,” “magic,” and “mystery.” At this point, I’ll just say that M-theory is still a “Missing theory” which is postulated but not fully understood. However, even though M-theory still leaves many questions unanswered, the advances made with branes revealed theoretical connections that called for M-theory’s more complex, more enveloping structure. That is why string theorists study it today.

This chapter updates the string theory picture that began in the 1980s, presenting some aspects of the more modern viewpoint that physicists developed in the 1990s. Much of this material will not be central to branes’ applications to particle physics, and later brane-world conjectures won’t explicitly rely on any of the phenomena described below. You should therefore feel free to skip ahead if you choose. But if you like, take this opportunity to get acquainted with some of the remarkable developments in string theory that were in large part responsible for placing branes squarely on string theory’s theoretical map.

Nascent Branes

In Chapter 3 we saw that branes extend over some, but not necessarily all, of space’s dimensions. For example, a brane might extend only over three dimensions of space, even if the bulk space contains many more. Extra dimensions might terminate on branes; in other words, branes can bound extra-dimensional space. We also know that a brane can house particles that move only along its dimensions. Even if there were many additional spatial dimensions, particles confined to a brane would move only along the more limited region occupied by that brane; they wouldn’t be free to explore the full extra-dimensional bulk.

We will now see that branes are more than just a location; they are objects in their own right. Branes are like membranes, and, like membranes, they are real things. Branes can be slack, in which case
they can wiggle and move, or they can be taut, in which case they will probably sit still. And branes can carry charges and interact via forces. Furthermore, branes influence how strings and other objects behave. All these properties tell us that branes are essential to string theory; any consistent string theory formulation must include branes.

In 1989, Jin Dai, Rob Leigh, and Joe Polchinski, all then at the University of Texas, and independently the Czech physicist Petr Hořava, mathematically discovered a particular type of brane called a D-brane in the equations of string theory. Whereas closed strings loop around, open strings have two free ends. These ends have to be somewhere, and in string theory the allowed locations for open string ends are D-branes (the “D” refers to Peter Dirichlet, a nineteenth-century German mathematician). The bulk can contain more than one brane, so not all strings necessarily end on the same brane. But Polchinski, Dai, Leigh, and Hořava discovered that all open strings have to end on branes, and string theory tells us what dimensions and properties these branes will have.

Some branes extend in three dimensions, but others extend in four or five or more dimensions. In fact, string theory contains branes that extend in any number of dimensions up to nine. The string theory convention for labeling branes is to use the number of dimensions of space—not of spacetime—in which they extend. For example, a 3-brane is a brane that extends through three dimensions of space (but four dimensions of spacetime). When we come to look at the consequences of branes for the visible world, 3-branes will be very important. However, for the applications of branes discussed in this chapter, branes with other numbers of dimensions will also play a role.

Different types of brane arise in string theory. They are distinguished not only by their dimensionality—the number of dimensions in which they extend—but also by their charges, their shape, and an important characteristic called
tension
(which we’ll get to soon). We don’t know whether branes exist in the real world, but we do know the types of brane that string theory says are possible.

Branes were just a curiosity at the time they were discovered. Back then, no one saw any reason to include branes that interacted or moved. If strings interacted only weakly, as string theorists initially assumed, D-branes would be so taut that they would just sit there and
not contribute to string motion or interactions. And if branes don’t respond to strings in the bulk, they would just be an unnecessary complication. They would be a place or location, but they would be no more relevant to the motions and interactions of strings than the Great Wall of China is to your daily existence. Moreover, physicists didn’t want to include branes in a physical realization of string theory because branes violated their intuition that all dimensions are created equal. Branes distinguish certain dimensions—those along the brane are different from those that extend off it—whereas the known laws of physics treat all directions the same. Why should string theory be different?

We also expect physics at any one point in space to be the same as it is at any other. But branes don’t respect this symmetry either. Although branes extend infinitely far along some dimensions, they are situated at a fixed position in the other directions. That is why they don’t span all of space. But in those directions in which the brane’s position is fixed, an inch from the brane is not the same as a yard or a half-mile from the brane. Imagine a brane that was drenched in perfume. You would definitely be able to tell whether you were near it or far from it.

For these reasons, string theorists initially ignored branes. But about five years after branes were discovered, their status in the theoretical community dramatically improved. In 1995 Joe Polchinski irreversibly changed the course of string theory when he showed that branes were dynamical objects that were integral to string theory and were likely to play a critical role in its ultimate formulation. Polchinski explained what types of D-brane are present in superstring theory, and demonstrated that these branes carry charge
²⁸
and therefore interact.

Moreover, the branes in string theory have finite tension. Brane tension is akin to the tension of the surface of a drum that returns to its taut position after you pinch it or punch it. If a brane’s tension were zero, any small touch would have an enormous effect since the brane would have no resistance. On the other hand, if a brane’s tension were infinite, you couldn’t have any effect on it in the first place, for it would be a stationary object, not a dynamical one. Because the tension of branes is finite, branes can move and fluctuate and respond to forces, just like any other charged object.

Branes’ finite tension and nonzero charge tell us that they are not merely places, they are also things: their charges tell us that they interact, and finite tension tells us that they move. Like a trampoline—a surface that interacts with its environment when it is depressed and when it springs back—a brane can move and interact. For example, both trampolines and branes can be distorted. And both trampolines and branes can influence their surroundings, trampolines by pushing on people and air, and branes by pushing on charged objects and the gravitational field.

If branes exist in the cosmos, their violation of spacetime symmetries should be no more disturbing than the violation of spatial symmetries caused by the Sun or the Earth. The Sun and the Earth are also located in particular locations; when measured with respect to the Sun or the Earth, not all positions in three-dimensional space are the same. Nonetheless, physical laws preserve the spacetime symmetries of three-dimensional space, even if the state of the universe does not. Branes would be no worse than the Sun or the Earth in this respect. Branes, like all other objects at definite places in space, break some symmetries of spacetime.

A moment’s reflection reveals that this is not such a bad thing. After all, if string theory is the true description of nature, then not all dimensions are created equal. The three familiar spatial dimensions look alike, but the extra dimensions must be different; if they weren’t, they wouldn’t be “extra.” From the vantage point of the physical universe, the violation of spacetime symmetries could help explain why extra dimensions are different: branes might correctly distinguish string theory’s extra dimensions from the three spatial dimensions we experience and know.

In later chapters, I will consider branes with three spatial dimensions and describe some of their potentially radical implications for the real world. But for the rest of this chapter we’ll concentrate on why branes are so significant in string theory—so important, in fact, that they catalyzed the “second superstring revolution” of 1995. The next section gives a few reasons why branes have remained at the forefront of string theory for the past decade, and why we now think they’re here to stay.

Mature Branes and the Missing Particles

While Joe Polchinski was hard at work investigating D-branes, Andy Strominger, then his colleague at Santa Barbara, was pondering
p-branes
—fascinating solutions to Einstein’s equations. They expand infinitely far in some spatial directions, but in the remaining dimensions they act as black holes, trapping objects that come too close. D-branes, on the other hand, are surfaces on which open strings end.