There is a seeming paradox if you try to introduce magnetic monopoles into a chiral gauge theory, including the Standard Model. The chiral nature of the theory means that the ingoing scattering modes carry different quantum numbers from the outgoing modes. The challenge is to find a way to consistently turn the ingoing modes into outgoing modes while preserving the gauge symmetries. The seeming paradox is that there is no way to do this.
I will review this paradox and explain recent work on how to resolve it. The resolution is rather dramatic: the monopole acts as a portal to a twisted sector of Hilbert space, where fermions carry different quantum numbers.
Laura Cardani, Angelo Esposito, Valerio Ippolito