## Friday, May 04, 2007 ... //

### Solving the planar limit of N=4 gauge theory: press releases

Since the visionary discoveries of 't Hooft in the 1970s, it's been known that gauge theories with a large number of colors should simplify and lead to a new kind of classical limit. Whenever the number of some objects is large, physics should simplify. Statistical physics simplifies into thermodynamics if you deal with many atoms. If you investigate theories with many colors, you should expect a simplification, too.

Indeed, shortly after the relevance of QCD for strong interactions was appreciated, 't Hooft has figured out that the most important Feynman diagrams start to look like a discretization of a two-dimensional surface - something we would call the worldsheet these days - that describes a history of propagating one-dimensional loops of energy, strings. ;-)

Gerard 't Hooft found out that whenever the number of colors is large, the Feynman diagrams can be split into groups according to the topology of the corresponding worldsheet that they discretize. The simplest topology, namely the "planar" topology, dominates while the more complicated topologies with "handles" are suppressed by powers of 1/N^2. The strict large-N limit is equivalent to strictly continuous worldsheets replacing Feynman diagrams.

This discovery was important for conceptual reasons - gauge theories are theoretically important even if the number of colors doesn't match the real world. But it was also important for observable physics because for QCD, 1/N^2 is 1/9 which is a small number and the new kind of stringy expansion could thus be useful.

Some key details about the behavior of the gauge theory at a large number of colors remained unknown for more than 20 years - until 1997 when Juan Maldacena famously merged 't Hooft's ideas with holography and new insights about black hole thermodynamics: the string theory describing the large-N limit of gauge theories has one additional large dimension besides those seen in the gauge theory and it includes strings and all other objects in an anti-de-Sitter space. Conformal symmetry, including the Lorentz symmetry, translations, scalings, and special conformal transformations, is interpreted as an ordinary isometry of the anti de Sitter space.

Integrability and media

That's great but can we actually calculate how these strings interact in the large N limit? Can we solve the planar limit i.e. to find all possible excitations on the corresponding string and the interactions of these excitations? In recent years, this question has been answer Yes.

of Princeton University has promoted the paper by Klebanov et al. that has numerically verified hypotheses of Bern et al. and especially integral equations by Beisert et al. about the behavior of the N=4 gauge theory in the planar limit, based on the concept of transcendentality.
See Juan Maldacena and integrability and links in that article...
Now, I think that the press release is an example of news that the journalists should propagate much more intensely than they do - and they should think how to make them more attractive than they sound in the present form. The press release talks about serious work that is actually viewed to be exciting by the actual big shots who are respected by some of the brightest people, not just by journalists and their least demanding readers, and it uses honest language to analyze its numerous aspects of the relation between gauge theories and string theory.

These relations between gauge theory - an experimentally well-established pillar of modern physics - and string theory, together with the unity of string theory itself, are the main reason why string theory can never go away in the future, and only people unfamiliar with the structure of theoretical physics could think otherwise.

Controversial terminology

The only bizarre feature of the press release is the formulation at the beginning that "string theory is both one of the most promising and controversial ideas in modern physics." A nice politically correct formulation to make many crackpots happy. Is any theory whose critic is able to impress dozens of journalists automatically controversial? If it is, isn't the adjective "controversial" somewhat vacuous?

Well, I don't think that any of these calculations that tightly connect physics of gauge theory with numerous concepts and equations of string theory are controversial. Most people who like to create controversies would probably find these papers rather boring. What is really controversial is the stupid caricature of modern physics that has been invented by a few evil people and promoted by their friendly journalistic jerks.

But once again, that's very different from the actual scientific results that are somewhat intimidating and, as far as I can say, almost certainly right.

And that's the memo.