The odd thing is that there are a lot of mathematical connections between string theory and the loop representation. Gradually, as time went on, I became more and more convinced that maybe the layfolk were right – maybe the loop representation of quantum gravity really WAS string theory in disguise, or vice versa. This made a little embarrassed by how much I had been making fun of string theory.

I decided to write a paper about this, and as I did some research I was intrigued to find more and more connections between the two approaches, to the point where it is clear that while they are presently very distinct, they come from the same root, historically speaking.

So what I’m hinting at, in brief, is that a bunch of category theory may provide the links between modern string theory with its conformal fields and the loop representation of quantum gravity. This is not as outre as it may appear. The categories being discussed here are really just ways of talking about symmetries (see my stuff on categories and symmetries for more on this). As usual in physics, the clearest way to grasp the connection between two seemingly disparate problems is often by recognizing that they have the same symmetries.

September 11, 1993
This Week’s Finds in Mathematical Physics (Week 18)
John Baez

2011.03.31 Thursday ACHK