Black Holes and Beyond: Harvard’s Andrew Strominger on String Theory

So how did you derive the entropy calculation?

Strominger: What Vafa and I were doing, in effect, was fishing. We looked at all possible kinds of black holes in order to find one for which we could actually do the computation. The first example we could solve was in five dimensions–although by now many other cases, including four dimensions, have been solved. We found that we were able to give a complete description of a five-dimensional black hole by building it out of strings and microscopic objects called D-branes, which were discovered in 1995 by Joe Polchinski of UC Santa Barbara. So, in essence, we gave a microscopic description of a black hole in terms of some more fundamental building blocks. When the dust had settled, it turned out that the thing that described the black hole was a system called a conformal field theory. This was a field theory that lived on a circle, which means it has one spatial dimension and one time dimension. We derived the fact that the quantum states of the black hole could be represented as the quantum states of this one-plus-one dimensional quantum field theory, and then we counted the states of this theory and found they exactly agreed with the Bekenstein-Hawking entropy.

High-Impact Papers by Andrew Strominger
Published Since 1985
(Ranked by average citations per year)

Rank	Paper	Total Citations	Average cites per year
1	A. Strominger, C. Vafa, "Microscopic origin of the Bekenstein-Hawking entropy," Phys. Lett. B, 379(1-4):99-104, 1996.	490	163
2	P. Candelas, et al., "Vacuum configurations for superstrings," Nucl. Phys. B, 258(1):46-74, 1985.	1,538	110
3	C.G. Callan, et al., "Evanescent black holes," Phys. Rev. D, 45(4):1005-9, 1992.	519	74
4	D. Garfinkle, G.T. Horowitz, A. Strominger, "Charged black holes in string theory," Phys. Rev. D, 43(10):3140-3, 1991	370	46
5	A. Strominger, "Massless black holes and conifolds in string theory," Nucl. Phys. B, 451(1-2):96-108, 1995.	139	40

SOURCE: ISI's Science Citation Report, 1981-98.

Does this imply that you now have two descriptions of the black hole–one in string theory and one in general relativity?

   Strominger: Yes. One of these descriptions is the familiar one–as an object with an event horizon, described by some solution of field equations. The other was as this one-plus-one dimensional conformal field theory. These are the two descriptions, and we showed that these two descriptions agreed–that is, they gave the same answer for the entropy. So we started trying to build a more precise dictionary relating these two descriptions of the same fundamental object. Then the plot thickened. Vafa and I had only computed the entropy of a black hole in its ground state, but there are plenty more things we'd like to understand. We could excite the black hole, for instance, and compute what's called the Hawking radiation. We already know how to do that using Hawking methods in the picture where the black hole is space-time curvature. One would like to do it in the other picture where the black hole is a one-plus-one dimensional field theory. Juan Maldecena and I–Juan is now at Harvard–and other people, including Sumit Das of the Tata Institute and Samir Mathur of MIT, found that this one-plus-one dimensional field theory was good for a lot more than just counting the ground states. Indeed, it was giving us a much better description of the quantum dynamics of black holes than we had ever anticipated.
   Then, in November of 1997, Juan found a systematic way of going between the description of the black hole as very strong curvature of space time and the description as this one-plus-one-dimensional field theory. What he found was that under certain conditions there is this exact duality–a kind of exact correlation–between conformal field theory in one-plus-one dimensions and string theory on what's called the near-horizon geometry of the black hole, which is the highly curved space right at the horizon of the black hole.
   In general, Juan's work tells us that in some cases theories of gravity are the same thing as quantum field theories looked at in the proper way. And that's very interesting because quantum field theory and gravity-general relativity are two of the main accomplishments of theoretical physics in the 20th century, and we're now seeing that at least in some cases they are really two sides of the same coin.

Does this mean you're getting to a point where you could soon test the theory?

Strominger: No, it still goes without saying that we don't have experimental evidence for string theory and we don't have a sure proposal for an experiment that will definitively test the theory. Although we could get lucky.

So what makes you think you're on the right track?

Strominger: Well, there are other ways that our confidence in string theory has been bolstered. One is the black hole story, in that Boltzmann's work in the 19th century, which showed that the theory of molecules could explain the laws of thermodynamics, was in itself indirect evidence for that theory of molecules, and played some role in the eventual acceptance of the theory. It was not a definitive role. The definitive discovery was when scientists could basically see the molecules. In the same sense, the black hole story was an unsolved problem from what seemed to be another branch of physics not directly associated with string theory. Now string theory has provided an explanation for that, and it is the only really robust explanation that has been provided. That is indirect evidence for string theory, or at least evidence that we're moving in the right direction.
And then string theory is being used to solve other long-standing problems. Juan Maldacena's recent work is the most dramatic example of this. All of this seems to argue for the inevitability of string theory. It seems to be a theoretical structure that you can't escape; it bangs you on the head wherever you turn. I think that nature will avail itself of string theory in some way, although it's quite possible that our present picture of how that will happen is too naďve.

So what's the next step?

Strominger: I don't know. There are many directions that people are trying to go in. There's been some jump in our understanding of black holes, and, having identified the organizing principle for the low-energy dynamics of black holes, it gives a new way to think about some still-outstanding, very profound puzzles concerning these objects. I think there will be some progress there, although it's impossible to know. We've made enormous progress lately, but we can never know if we will continue to understand new things at the same rate or not. Unfortunately, it's like predicting the weather.