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.
