The Langlands Correspondence in Physics

[Jim Kata]

Does anybody understand how to put quantum field theory in terms of the geometric Langlands program? I'm kind of reading Witten's paper Quantum Field theory, Grassmanians, and algebraic curves. Also, the more recent work of Connes shows that his group of diffeographisms is motivic galois group. I have not read Witten and Kapustins mammoth paper. Any ideas about Langlands in physics? Teach me what you know. Mind you, my knowledge is very physics based so if you can't explain in physicsy terms what the ring of adele's is you might lose me.

 

[shoehorn]

Does anybody understand how to put quantum field theory in terms of the geometric Langlands program?

No. Nobody does. Indeed, that's rather like asking "Does anybody have a verifiable theory of quantum gravity?"

 

[Kea]

Does anybody understand how to put quantum field theory in terms of the geometric Langlands program?

Why geometric Langlands? Classical Langlands might be more relevant than the kind of continuum geometry that is studied as a result of, say, string theory prejudices.