Warped Passages - Lisa Randall [164]
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