# What evidence do we have for S-duality in N=4 Super-Yang-Mills?

Do we have anything resembling a proof*? Or is it just a collection of "coincidences"?

Also, do we have evidence from lattice gauge theory computations?

*Of course I'm not talking about a proof in the mathematical sense, only a compelling albeit heuristic argument e.g. an argument involving formal manipulations with path integrals.

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Just a quick feedback: I doubt there is something resembling a proof in a mathematical sense of anything at all for a fully fledged QFT (which has infinitely many states and divergences -- leading to non-trivial critical exponents), so I am not sure this is productive. Asking for evidence seems interesting though a bit broad, maybe there is a place to add some motivation. I am also not sure by what you mean by “numerical” and why you single out such evidence. – user566 Oct 26 '11 at 20:12
Thanks, much better. – user566 Oct 26 '11 at 20:59