What do monopoles have to do with strong coupling?

Question

My understanding is that strong coupling effects arise from instantons in the path integral.

But I sometimes read that monopoles (see the electric-magnetic duality) can allow one to calculate strong coupling effects. How do I reconcile this with my understanding that instantons are responsible for strong coupling effects?

A good starting point is these notes by 't Hooft: hep-th/0010225 However, be warned that there are some typos in the math. — Buzz, Jan 04 '23 at 03:24

score 1 · Answer 1 · answered Jan 04 '23 at 13:38

1

I guess the answer is: Instantons mediate (in time) between configurations of different winding number. This can be thought of as the creation or destruction of monopoles, since monopoles carry winding number.

Therefore, in a QFT of monopoles, where monopoles can be created and destroyed, instantons will naturally be accounted for, providing the non-perturbative physics.

answered Jan 04 '23 at 13:38

dennis

732

Actually I'm not satisfied with this answer for the following reason: the winding that the monopole carries (see here for instance) is not the same as the winding of the vacua between which the instanton mediates -- for instance, the monopole configuration carries a magnetic field while the vacuum obviously doesn't. So it is still not clear how a QFT of monopoles accounts for the instantons which are supposed to provide the non-perturbative physics. – dennis Jan 20 '23 at 12:58

What do monopoles have to do with strong coupling?

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