# Three questions on Montonen-Olive duality

1. Mar 12, 2014

### metroplex021

Hi folks -- I have three questions on Montonen-Olive duality. This duality switches the electric and magnetic couplings, where these couplings are related by the Dirac quantization condition

eg = 2$\hbar\pi$n

Here e is the electric charge and g the magnetic (monopole) charge.

1. First of all, do these couplings both 'run' in the theory (thus have their own, non-zero beta function)? If so, does that mean that there are energy regimes in which e is small and g large, and other regimes where g is small and e large?

2. It is said that, in one way of taking the classical limit, magnetically charged particles arise as composite particles while the electrically charged particles are fundamental, and yet in another way of taking the limit it's the electrically charged particles that are composite and the magnetic monopoles that are now elementary. In the first case, it's when e is taken to go to zero while g is held fixed as h tends to zero, and in the other case it is g that goes to zero while e is held fixed in the classical limit. Do any principles govern which of these limits is the right one to take? That is, do any facts about the physics of the situation inform you that it's g (or e) that should be held fixed in the h-> 0 limit?

3. Finally, why do we look at particle content in the classical limit anyway? Isn't the spectrum of a quantum field theory an intrinsic property of it, and moreover one that can be assigned in regimes of finite h?

Any help on any of these questions would be very much appreciated!!

metroplex