Ben Niehoff
Science Advisor
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tom.stoer said:So what is the background-independent formula fully defining string theory?
If you're now demanding the One Equation then I don't know what to tell you. That is a separate issue entirely, and I think string field theory is still not too well understood, except in a few generalities. Although I do think Witten wrote down an action for it involving Moyal star products.
The worldsheet action (as a SUSY, nonlinear sigma model) is a standard textbook thing, and you can look it up in, say, Becker, Becker, Schwarz.
As for M-theory, as far as I remember, people are still trying to work out what the actions of M2- and M5-branes might be.
I'm not sure the lack of a One Equation is even a problem. I don't see anyone being particularly bothered that QED has no full, non-perturbative definition.