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The second sentence of the Wikipedia article on $\mathcal{N} = 4$ supersymmetric Yang-Mills theory describes it as "a simplified toy theory." But the AdS/CFT correspondence conjectures that it is precisely dual to Type IIB string theory on the manifold $AdS_5 \times S(5)$, which is believed to in principle contain the complete dynamics of a full quantum theory of gravity - arguably currently the best candidate theory for capturing all known laws of physics. Isn't this literally the most exact possible opposite of a "simplified toy theory"?

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    $\begingroup$ Comment to the post (v1): The author(s) of the Wikipedia phrase "$\mathcal{N} = 4$ SYM is a simplified toy theory" likely don't imply anything with the chosen wording beyond that $\mathcal{N} = 4$ SYM does not describe the real world, i.e. it does not include a standard model sector. $\endgroup$ – Qmechanic Aug 3 '16 at 7:30
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$\mathcal N = 4$ SYM is useful to study aspects of perturbation theory, especially since exact solutions are known. It is not possible to describe our physical world with it though.

You mention the ADS/CFT duality to a String Theory on $AdS_5 \times S_5$. This background spacetime can not be the one we live in, as it can not be compactified to anything (close to) Minkowski space.

Since the theory is useful to learn about propoerties that realistic models might have, it is considered a "toy" model.

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