Schwinger pair production of magnetic monopoles

Electromagnetic duality implies that strong magnetic fields will produce magnetic monopoles by the dual Schwinger effect, if indeed magnetic monopoles exist. As a consequence, strong magnetic fields provide perhaps the best avenue to search for magnetic monopoles: the existence of any given strong magnetic field provides a lower bound on their mass. This search strategy has recently been utilised at the LHC, where the strongest known magnetic fields are produced fleetingly by heavy-ion collisions. In these fields calculations of the monopole production cross section must go beyond the locally-constant field approximation. I will discuss recent theoretical progress in carrying out this calculation, as well as open theoretical questions. I will also comment on the relation between the probability of Schwinger pair production of magnetic monopoles and a well-known “exponentiation conjecture” for the imaginary part of the Euler-Heisenberg Lagrangian to all loop orders.