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By Root 2037 0

from Chapter 4 that low-energy strings are well described by point particle quantum field theory, and that is the case here. The particular kind of quantum field theory involves a number of sophisticated mathematical ingredients (and it has an ungainly characterization: conformally invariant supersymmetric quantum gauge field theory), but two vital characteristics are readily understood. The absence of closed strings ensures the absence of the gravitational field. And, because the strings can move only on the tightly sandwiched three-dimensional branes, the quantum field theory lives in three spatial dimensions (in addition to the one dimension of time, for a total of four spacetime dimensions).

The remaining part of the second description consists of closed strings, executing any vibrational pattern, as long as they are close enough to the black branes’ event horizon to appear lethargic—that is, to appear to have low energy. Such strings, although limited in how far they stray from the black stack, still vibrate and move through nine dimensions of space (in addition to one dimension of time, for a total of ten spacetime dimensions). And because this sector is built from closed strings, it contains the force of gravity.

However different the two perspectives might seem, they’re describing one and the same physical situation, so they must agree. This leads to a thoroughly bizarre conclusion. A particular nongravitational, point particle quantum field theory in four spacetime dimensions (the first perspective) describes the same physics as strings, including gravity, moving through a particular swath of ten spacetime dimensions (the second perspective). This would seem as far-fetched as claiming … Well, honestly, I’ve tried, and I can’t come up with any two things in the real world more dissimilar than these two theories. But Maldacena followed the math, in the manner we’ve outlined, and ran smack into this conclusion.

The sheer strangeness of the result—and the audacity of the claim—isn’t lessened by the fact that it takes but a moment to place it within the line of thought developed earlier in this chapter. As schematically illustrated in Figure 9.5, the gravity of the black brane slab imparts a curved shape to the ten-dimensional spacetime swath in its vicinity (the details are secondary, but the curved spacetime is called anti–De Sitter five-space times the five sphere); the black brane slab is itself the boundary of this space. And so, Maldacena’s result is that string theory within the bulk of this spacetime shape is identical to a quantum field theory living on its boundary.15

This is holography come to life.

Maldacena had built a self-contained mathematical laboratory in which, among other things, physicists could explore in concrete detail a holographic realization of physical law. Within a few months, two papers, one by Edward Witten and one by Steven Gubser, Igor Klebanov, and Alexander Polyakov, supplied the next level of understanding. They established a precise mathematical dictionary for translating between the two perspectives: given a physical process on the brane boundary, the dictionary showed how it would appear in the bulk interior, and vice versa. In a hypothetical universe, then, the dictionary rendered the holographic principle explicit. On the boundary of this universe, information is embodied by quantum fields. When the information is translated by the mathematical dictionary, it reads as a story of stringy phenomena happening in the universe’s interior.

Figure 9.5 A schematic illustration of the duality between string theory operating in the interior of a particular spacetime and quantum field theory operating on the boundary of that spacetime.

Figure 9.6 The holographic equivalence applied to a black hole in the bulk of spacetime yields a hot bath of particles and radiation on the region’s boundary.

The dictionary itself renders the holographic metaphor all the more appropriate. An everyday hologram bears no resemblance to the three-dimensional image it produces. On its surface appear