## Thursday, February 26, 2009

### History of Yang-Mills theory and wishful thinking

The readers of a notorious anti-physics blog are discussing the history of Yang-Mills theory. The basic historical facts about the fathers and grandfathers of non-Abelian gauge theory are not difficult to summarize:
• the theory was almost completely constructed by Oskar Klein (TRF) in the late 1930s; it's because this superbright guy was able to learn some general lessons about gauge theories from the Kaluza-Klein theory he co-fathered; it was one of the early examples of string theory's ability to penetrate from the future into the past and give selected physicists an extraordinary ability to be ahead of everyone else
• the theory was completely constructed by another superbright guy, Wolfgang Pauli, in the 1940s; but he didn't publish it because he was also able to "prove" that because of the new long-range forces, the theory was ruled out (of course, he knew neither the symmetry breaking nor the confinement)
• the complete classical theory was published in 1954 by Yang and Mills but all the details of their physical motivation were incorrect (and they didn't know the Higgs mechanism and the confinement either)
The application of these non-Abelian gauge theories on reality arguably didn't make much progress between the 1930s and the late 1950s. Back in 1954, Yang and Mills had the following applications in mind:
• like everyone else, they dreamed about describing the strong interactions - which was so mysterious
• they decided that the SU(2) isospin had to be a local symmetry.
As you know, the latter point rather quickly led to the electroweak theory - a new description of the weak and electromagnetic interactions with an SU(2), isospin-like (but chirally coupled) factor of its gauge group. Tasked by his advisor Julian Schwinger, Sheldon Glashow (and others) began to publish papers about this SU(2) origin of the weak interactions in 1956, just two years after the 1954 Yang-Mills paper.
On the other hand, the application of Yang-Mills theory to the strong interactions had to wait for nearly 20 more years (or 35 years since Klein's insights), until the early 1970s. The gauge group had to be changed (and constructed from the scratch), it had to be disconnected from the isospin because the isospin is just an approximate global symmetry of the strong force, and asymptotic freedom had to be understood.

You can see that the two points listed above - the dream of Yang and Mills to explain the strong force; and their decision to gauge the isospin - have nothing to do with each other. That's why the statement that they constructed their theory to describe the strong force is untrue. They were dreaming about an explanation of the strong force but every detail they did with their theory was only relevant for a better description of the weak force!

Their wishful thinking - that had nothing to do with their actual results - is only relevant for the historians of science. But a general lesson may be relevant for the physicists, too. Theories are often discovered with a different purpose in mind. Yang and Mills wanted to understand the strong force but their detailed results were directly relevant as a starting point for a new electroweak theory only.

After two more decades, a modified version of their theory became essential for the strong force, too.

The case of string theory is of course completely analogous. It was also invented to explain some patterns of the strong force. In doing so, the old string theory was arguably much more successful than the paper of Yang and Mills. However, it was too predictive, too UV soft, and these predictions of the old string theory made it uninteresting for the particle physicists focusing on the strong force.

Much like Yang-Mills theory was reclassified in 1956 from a theory of the strong force to a theory of the electroweak force, string theory was reclassified in 1974 (by Scherk and Schwarz; and by Yoneya) from a theory of the strong force to a theory of quantum gravity where its spectrum and interactions seemed to be directly (and miraculously) relevant.

However, the 1973 discovery (by Gross, Wilczek, and Politzer) of asymptotic freedom made Yang-Mills theory relevant for the strong force, too. Analogously, the 1997 discovery (by Maldacena) of the AdS/CFT correspondence has also made string theory relevant for the strong force, by refining and clarifying some older insights due to 't Hooft. Maldacena's findings also implied that gauge theory and string theory were really the same thing, at least in some superselection sectors.

So the original intentions of the fathers of Yang-Mills theory and string theory became reality.

Why is it true that physical theories and mathematical structures can transform their application as the history progresses? We usually don't expect a washing machine to become useful as a fridge. Well, the difference is that physical theories and mathematical structures are not being invented; they're there; they are only being discovered.

In what universe? In all of them: that is the point! :-) [TBBT.]

Coraline, a 3D film. A girl finds a happier parallel world, apparently in the extra dimensions. Via David Berenstein.

So we are somewhat similar to a primitive tribe that finds a washing machine (produced by someone else). At the beginning, they will use it as a fridge. As their knowledge increases, they will learn how to do the laundry. However, if they become even more skillful, they may update the device a bit - or press a hidden button - and use it as a fridge, too. I didn't tell you: it was one of the washing machines that can also cool the clothes down. :-)

While a washing machine that can cool things down may look uneconomic, Nature has different criteria for the economy. It loves to recycle the ideas and the same underlying idea is often able to do many jobs at the same moment.