Condensed matter physics is full of approximations, where one avoids a problem by enlargin the Hilbert space, analogous to AdS/CFT.
One hope is to use integrable models, which one can solve exactly no matter what coupling is. Many physical systems are approximately integrable. Conformal field theories play a similar role.
An obvious example would be QCD that has obvious importance in the Standard Model
Dualities may help a lot and may be not just AdS/CFT. There may be new opportunities arising in math. The examples we have so far are solutions for special cases and particular theories. Integrability in these examples is key.
“I can only express my disappointment. I don't know how many years it's been since we developed QFT... but even now, if we want to handle quantum field there, we still have to do perturbation theory.”
But saying something is strongly coupled is describing it as “not tractable by perturbation theory.” In other words, we're describing it by what it's not. It's better to describe something by the phenomenon it represents. A strongly interacting system might mean highly entangled and that's interesting. And thinking about how to describe entanglement offers a path into how to handle that type of strongly coupled system. In other words, think about how to understand the phenomenon that's happening rather than how to handle the general problem of “no perturbation theory.”
Effective theories, QCD... [?]
Strong coupling is tractable in integrable systems (N=4 SYM, spin chains). QCD and N=4 SYM have deep connections maybe. Use resumming for QCD?
Just use numerics? E.g. lattice QCD. And these methods can give us qualitiative insights and surprises.
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