String theory may be able to explain what goes on inside some of the most useful materials on Earth.

# Tying up some loose ends

String theory: you love it or loathe it. To some it represents our best hope for a route to a "theory of everything"; others portray it as anything from a mathematically obtuse minefield to a quasi-religion that has precious little to do with science. There might be a middle way. String theory's mathematical tools were designed to unlock the most profound secrets of the cosmos, but they could have a far less esoteric purpose: to tease out the properties of some of the most complex yet useful types of material here on Earth.

Both string theorists and condensed matter physicists - those studying the properties of solids, liquids and so on - are enthusiastic. "I am flabbergasted," says Jan Zaanen, a condensed matter theorist from the University of Leiden in the Netherlands. "The theory is calculating precisely what we are seeing in experiments." If solid science does turn out to be the salvation of string theory, it would be the latest twist in a tangled history. String theory was formulated in the late 1960s to explain certain features of the strong nuclear force, one of four fundamental forces of nature. It holds that electrons, quarks and the like are not point-like particles but minuscule, curled-up, vibrating strings.

No sooner had this idea emerged, though, than it lost ground to particle physicists' "standard model", which proved capable of describing not just the strong force but also the weak and electromagnetic forces - and did so far more intuitively. Then string theory staged a dramatic comeback when gravity resisted incorporation into the standard model, still being described by Einstein's general theory of relativity, a resolutely non-quantum theory.

But progress has been abysmally slow. "The string theorists were saying, 'Give us two more weeks and we will have explained all the big puzzles in the universe'," Prof Zaanen observes. "That was 20 years ago." The critical voices have in the meantime been getting more strident. They complain about string theory's weird, unverifiable predictions - for instance, that space-time has any number of dimensions, usually 10, rather than the three of space and one of time we see. To its detractors, string theory is long on mathematical elegance, but woefully short on real-world relevance.

Enter a string theory curiosity with the forbidding moniker of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT for short) which is at first glance a classic of the genre. Dreamed up in 1997 by Juan Maldacena, a young Argentinian then working at Harvard University, it is a special case of what is known as the "holographic principle". The basic premise was this: much as a hologram you might find on your credit card encodes all the information for a 3D image in just two dimensions, a quantum theory in a certain number of dimensions that includes gravity can be encoded as an entirely different theory - without gravity - in one dimension fewer. The three spatial dimensions of our universe - along with gravity and us too - might, for instance, all be a holographic image generated from the interactions of particles on the cosmos's 2D boundary.

Prof Maldacena took that idea further. He was trying to do something that had consumed some of the best minds in cosmology for decades: to reconcile the behaviour of black holes, which are a core prediction of general relativity, with quantum theory. When he presented his work at a conference in Santa Barbara, California, in 1998, several hundred string theorists joined in with a specially composed song, The Maldacena, to the tune of the then-popular dance hit Macarena.

What possible relevance could this little-known theoretical conjuring trick have to the real world? Quite a lot, it seems, and in particular to the behaviour of certain types of condensed matter. That's where the tricks of the AdS/CFT correspondence come in handy. Though formulated for different circumstances, its mathematics provides a convenient bypass for a variety of problems. Take the exotic form of matter known as the quark-gluon plasma. In normal matter, quarks and gluons are bundled together into more familiar entities like protons and neutrons. At temperatures comparable with those seen in the immensely hot first microseconds of the universe, those bonds should break down, releasing a dense fireball of quarks and gluons acting in a similar way to the atoms of a gas, with few or no interactions between them.

That, at least, is what the field theory of the strong nuclear force predicts. But in 2005, when researchers at Brookhaven National Laboratory in Upton, New York, created a quark-gluon plasma by smashing together fast moving gold ions, they saw something very different. The plasma acted not as a gas, but as a superfluid - an almost perfectly flowing liquid with virtually no viscosity. Clearly, the interactions between the quarks and gluons of this exotic state were more complex than the standard theory could easily compute. But the AdS/CFT approach produced a close match to the experimental value - a triumph for a decidedly left-field approach.

Prof Zaanen pinpoints the moment at which his area got into bed with string theory as the publication of a paper in 2007 by the Harvard theorists Sean Hartnoll, Subir Sachdev and colleagues. It applied the AdS/CFT correspondence to high-temperature superconductors - in which electrons can flow without resistance, losing no energy as heat, at temperatures as mild as 150 degrees above absolute zero.

High-temperature superconductors behave as they do because of the way electrons organise themselves in the material, but 20 years and hundreds of thousands of research papers on from their discovery, we are no closer to knowing exactly how that is. The paper by Dr Hartnoll and his colleagues concerned an effect which AdS/CFT can model in just a few lines, rather than pages of dense algebra. It was the first time that an AdS/CFT calculation had been directly pitted alongside conventional methods and tested against a real experimental result in condensed matter - and the language of black holes came up with by far the more fluent answer.

High-temperature superconductors are not the only useful materials that might benefit from the AdS/CFT approach. Prof Sachdev has used the correspondence to compute properties of the plasma of electrons found in graphene - sheets of graphite a single atom thick. Once again, this could make string theory more relevant, since graphene has been touted as a successor to silicon as the stuff of microelectronics.