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By Root 2058 0

D-branes to compute D-entropy,” the crowd had reveled in a string theory version of the 1990s momentary dance craze, the Macarena—a touch more animated than Al Gore’s version at the Democratic National Convention, a touch less mellifluous than Los del Rio’s original one-hit wonder, but second to none in passion. I was one of the few at the conference whose talk was not focused on Maldacena’s breakthrough, so when I took the stage the next morning I felt it only appropriate to preface my remarks with a personal gesture of appreciation.

Now, more than a decade later, many would agree that no work in string theory since is of comparable magnitude and influence. Of the numerous ramifications of Maldacena’s result, one is directly relevant to the line we’ve been following. In a particular hypothetical setting, Maldacena’s result realized explicitly the holographic principle, and in doing so provided the first mathematical example of Holographic Parallel Universes. Maldacena achieved this by considering string theory in a universe whose shape differs from ours but for the purpose at hand proves easier to analyze. In a precise mathematical sense, the shape has a boundary, an impenetrable surface that completely surrounds its interior. By zeroing in on this surface, Maldacena argued convincingly that everything taking place within the specified universe is a reflection of laws and processes acting themselves out on the boundary.

Although Maldacena’s method may not seem directly applicable to a universe with the shape of ours, his results are decisive because they established a mathematical proving ground in which ideas regarding holographic universes could be made explicit and investigated quantitatively. The results of such studies won over a great many physicists who had previously eyed the holographic principle with much misgiving, and thus set off an avalanche of research that has yielded thousands of articles and considerably deeper understanding. Most exciting of all, there’s now evidence that a link between these theoretical insights and physics in our universe can be forged. In the next few years, that link may very well allow the holographic ideas to be experimentally tested.

The rest of this and the next section will be devoted to explaining how Maldacena achieved this breakthrough; the material is the most difficult we will cover. I’ll begin with a short summary, a CliffsNotes version that doubles as a guilt-free pass to jump to the last section should, at any point, the material overwhelm your appetite for detail.

Maldacena’s inspired move was to invoke a new version of the duality arguments discussed in Chapter 5. Recall the branes—the “slice of bread” universes—introduced there. Maldacena considered, from two complementary perspectives, the properties of a tightly stacked collection of three-dimensional branes, as in Figure 9.4. One perspective, an “intrinsic” perspective, focused on strings that move, vibrate, and wiggle along the branes themselves. The other perspective, an “extrinsic” perspective, focused on how the branes influence their immediate environment gravitationally, much as the sun and the earth influence theirs. Maldacena argued that both perspectives describe one and the same physical situation, just from different vantage points. The intrinsic perspective involves strings moving on a stack of branes, while the extrinsic perspective involves strings moving through a region of curved spacetime that’s bounded by the stack of branes. By equating the two, Maldacena found an explicit link between physics taking place in a region and physics taking place on that region’s boundary; he found an explicit realization of holography. That’s the basic idea.

With more color, the story goes like this.

Consider, Maldacena says, a stack of three-branes, so closely spaced that they appear as a single monolithic slab—Figure 9.4—and study the behavior of strings moving in this environment. You’ll recall that there are two types of strings—open snippets and closed loops—and that the endpoints of open strings can move