[zachf]

I agree with everything you said in the first two paragraphs. But string theory is not “motivated by nothing but cool looking math”. String theory is the generalization of quantum mechanics to higher dimensional fundamental objects, i.e. beyond particles, but in many senses the string theories that are well understood are just quantum mechanics in a different suit and hat.

It is already known that many of the most physically important quantum field theories are actually string theories if you rewrite them in different variables (this is called AdS/CFT duality), especially for understanding their large-coupling behavior string theory is the only tool available to analytically understand the theory. So string theory being completely wrong would be as surprising as quantum computing being impossible, for the same reason as you gave for QC. It would indicate something profoundly wrong about something we think we understand well. Its not impossible but the case is much, much more robust than the general internet understands.

[tsimionescu]

My point about string theory is exactly what you're saying: string theory is a different matehmatical formulation of QM, that happens to permit additional phenomena that have not been observed. It being a generalization to higher-dimensional spaces is exactly my point: it is mathematically motivated, not motivated by observation.

And yes, to the extent that it's the same formulae as QM, finding counter-example would be fascinating. But (higher-dimensional) string theory could be wrong with no impact on QM/QFT.

[zachf]

Well my main point is that AdS/CFT duality is asserting an exact equivalence between quantum field theories and string theories. So for example N=4 SYM, a quantum field theory viewed from one perspective, is exactly equal to a string theory from another perspective. That’s why I say it would be a spectacularly weird thing if string theory turned out to be unphysical but SYM was, because it would turn out then that they weren’t equal, and we really strongly believe they are.

In other words I’m not saying that string theory is (only) a generalization of known correct physics, but that many string theories are equal to (and therefore by definition as physically valid as) physically important quantum field theories. Then there are other string theories that are truly interesting and novel, too.

[tsimionescu]

Looking into this a little, AdS/CFT correspondence is only a conjecture, not a proven fact. More importantly, there are no AdS/CFT solutions that actually work with 4-dimensional curved space time, the working models are all in known non-physical geometries.

[zachf]

It’s a very strongly supported conjecture, but it has not been proven rigorously. As I said it would be extremely surprising if It were not true because of a frankly absurd amount of evidence. The second claim you make is false though— 3D holographic CFTs would be dual to a 4D quantum gravity theory.

Additionally, this conjecture is actually experimentally verifiable—you can set up strongly coupled systems in the lab and study the string theory description, and compare the predictions.