Understanding Confinement

This week and next there’s an interesting summer school going on at the IAS, with topic Understanding Confinement. Videos of talks are available here or at the IAS video site.

Taking a look at some of the first talks brings back vividly my graduate student years, which were dominated by thinking about this topic. When I arrived in Princeton in 1979, the people there had been working for several years on trying to understand confinement semi-classically, in terms of instantons and other solutions to the Yang-Mills equations (e.g. merons). By 1979 it had become clear that such semi-classical calculations were not sufficient to understand confinement and people were looking for other ideas. There were quite a few around, including the idea that there was some sort of string theory dual to pure Yang-Mills theory, and I spent quite a lot of time reading up on efforts of Migdal, Polyakov and others to find a formulation of string theory that would provide the needed dual. I ended up writing my thesis on lattice gauge theory, an approach which had the great advantage that you could at least put the calculation on a computer and start trying to get a reliable result for pure Yang-Mills numerically. Some of the calculations I did were done at the IAS, with Nati Seiberg and others. The other thing I spent a lot of time thinking about was how to put spinor fields on the lattice, the beginning of my interest in the geometry of spinors.

I strongly recommend watching Witten’s talk on Some Milestones in the Study of Confinement. His career started a few years before mine, with the early part very much dominated by the problem of how to make sense of Yang-Mills theory non-perturbatively, and this has has always been a motivating problem behind much of his work. In his talk he explains clearly the approaches to the problem (lattice gauge theory, 1/N, dual Meissner) that appeared very soon after the advent of QCD in 1973. He emphasizes how each of these approaches shows indications of a possible string theory dual, while frustratingly not leading to a string model that has the right properties, summarizing (41:30) the situation with:

The string theory we want is probably quite unlike any that we actually know, as of now. We don’t know how to make a string theory with the short distance behavior of asymptotic freedom.

In his talk he discusses later developments, in particular the Seiberg-Witten solution to N=2 SYM and the AdS/CFT duality between a string theory and N=4 SYM, explaining how these advances still don’t provide a viable approach to the confinement problem in pure Yang-Mills.

I’m looking forward to seeing the rest of the talks, and finding out more about some things that have happened over the years since I was most actively paying attention to what was happening with the confinement problem.