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Witten emphasises (in the Q&A session after his talk on introductory knot theory) that he works on theories which admit magnetic monopoles.

But how would the theories break down if magnetic monopoles do not exist? What are the theories that he eludes to?

$\mathsf{NOTE}$: I am well aware that there is a related question here which asks why contemporary physicists believe in the existence of monopoles, but it isn't similar.

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  • $\begingroup$ One of his indication is in fact towards the Seiberg-Witten theory. Where the The solutions of the Seiberg–Witten equations are called monopoles. $\endgroup$ – AMS Oct 30 '16 at 14:01
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    $\begingroup$ I think you already answered your question: He works on theories which admit magnetic monopoles. Therefore, those theories describe a world in which magnetic monopoles exist. I'm not sure what there is to elaborate. $\endgroup$ – ACuriousMind Oct 30 '16 at 15:29
  • $\begingroup$ The theories he's alluding to are string theory and Yang-Mills-Higgs theories with more symmetry than the Standard Model, such as grand unified theories. $\endgroup$ – user1504 Oct 30 '16 at 23:33

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