If not string theory, what is your unified theory of everything?

Update: The text below out of date. Recently I have a proposal (quite incomplete) for an approach to unification using twistor geometry. This proposal is described in this blog posting, and in detail here.

Older text:

I don’t have such a theory, and agree that the lack of good ideas is the strongest argument in favor of the continued pursuit of not very good ones like string theory unification.

In general terms though, I think the lesson of the last forty years is that the Standard Model has turned out to be far better than people have thought. Given this, it seems like a good idea to take it seriously as a truly fundamental theory, not just a low energy approximation to something different and better. There is much that we still don’t understand about the Standard Model, especially outside of perturbation theory. Much of the physics of QCD remains a mystery. Outside of perturbation theory, the behavior of the electroweak interactions is not understood, with, as far as I can tell, no completely consistent non-perturbative formulation of the theory. Working on these problems is not popular because they are very hard.

Personally I’m fascinated by the amazing deep relationships between fundamental mathematical issues in representation theory and the formalism of gauge fields, spinors and the Dirac operator that make up the SM. A better understanding of these relationships may very well teach us either something new about mathematics, or something new about physics.

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