Measured Against Reality

Thursday, October 18, 2007

String Theory may be useful after all

Here's an interesting string theory article from Nature (subscription required, sadly). It's about how string theory may be an accurate description of the strong force, what it was originally invented to explain.

Over the summer I took some high schools kids to talk to Leonard Susskind, a Stanford Professor and one of the developers of string theory. He described its original formulation as a theory of the strong force. One of the rationales he gave for thinking like this is that it's impossible to spin apart a nucleon. By that he meant that if you take anything bigger than a nucleon (say, a basketball), and spin it fast enough, it will break into constituent pieces. This is true for everything from a planet down to an atom. But when you spin a nucleon (proton or neutron) it doesn't break apart, but it does stretch out and turn into something like a dumbbell shape (and presumably gains a noticeable dipole moment). So one of the things that could explain that phenomenon is a force acting like a super-strong rubber band holding the constituent parts of the nucleon (quarks) together.

Anyway, that's the story given by someone who was there for why it was developed. The article gives a different description:

So particle physicists started casting around for other ways of attacking the problem. In 1968, the Italian theoretician Gabriele Veneziano made a brilliant guess and wrote down a concrete mathematical expression, the Veneziano amplitude, that explained some important features of high-energy scattering. But his formula could not be understood in terms of point-like particles; instead, it required the existence of extended objects — strings. These strings are thin tubes of energy formed by force lines that bind quarks together, and, just like violin strings, they can oscillate in many modes. The numerous resonances of strong-interaction physics would then be nothing but the different oscillation modes of these strings.

Here's a large chunk of the meat of the article:

The new approach that revives the link to string theory first suggested itself in 1998, when Juan Martín Maldacena conjectured a link between a close relative of QCD and a 'superstring' living in a ten-dimensional curved space-time. Although the theory in question, known as supersymmetric N = 4 gauge theory, is sufficiently different from QCD to be of no direct interest to experiment, the link raised the prospect of a general connection to some form of compactified string theory. This equivalence is now commonly referred to as the AdS/CFT (Anti-de-Sitter/conformal field theory) correspondence. If true, it would mean that string theory was originally not so far off the mark after all — its ingredients just need to be interpreted in the correct way.

The Maldacena conjecture raised a lot of interest, but seemed for a long time to be quantitatively unverifiable. This was because it takes the form of a duality in which the strongly coupled string theory corresponds to weakly coupled QCD-like theory, and vice versa. But to verify the duality, one would need to find a quantity to compare in a regime of intermediate coupling strength, and calculate it starting from both sides. No such quantity was obvious.

Help came from an entirely unexpected direction. Following a prescient observation, the spectrum of the N = 4 theory has been found1, 2 to be equivalently described by a quantum-mechanical spin chain of a type discovered by Hans Bethe in 1931 when modelling certain metallic systems. There are not many quantum-mechanical systems that can be solved analytically — the hydrogen atom is the most prominent example — but Bethe's ansatz immediately applied in a much wider context, and constructed a bridge between condensed-matter physics and string theory (in this context, see the recent News & Views article by Jan Zaanen on the nascent connection to high-temperature superconductivity). Indeed, even though the mathematical description of the duality on the string-theory side is completely different from that on the condensed-matter side, a very similar, exactly solvable structure has been identified here as well.

Puzzling out the details of the exact solution is currently an active field of research. But in one instance, that idea had already been put to such a hard test that a complete solution now seems within reach. The context is a special observable entity, the 'cusp anomalous dimension', which was argued to be ideally suited as a device to test whether string and gauge theory really connect. Some of its structure at strong coupling was also worked out. Just recently, Beisert, Eden and Staudacher have extracted the analogue of this observable on the field-theory side, and have been able to write down an equation valid at any strength of the coupling. Since then, work has established that their 'BES equation' does indeed seem, for the first time, to offer a means of reformulating theories such as QCD as string theories.

Much still needs to be learned from this one exactly solvable case. There is justifiable hope that this solution will teach us how to go back to the physically relevant case of QCD and finally arrive at the long-sought dual description by a string theory. It may even take us closer to realizing the quantum-field theorist's ultimate dream, unfulfilled for more than 50 years: completely understanding an interacting relativistic quantum-field theory in the four space-time dimensions that we are familiar with. Progress towards this goal can be judged independently of loftier attempts to use strings in the construction of a theory of everything.

So there's something, even if string theory isn't a theory of everything, it may yet be useful.



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