Confinement by monopole loops in inhomogeneous magnetic field

We show that a generalized Polyakov mechanism can lead to confinement at weak coupling in 3 + 1 dimensions when the theory is placed in a non-trivial, spatially varying magnetic field background. Depending on the magnitude of the field and the length scale of its spatial variation, the “dual” Schwinger mechanism for monopole-antimonopole pair creation may or may not be operative. At the threshold, monopole loops in the Euclidean description develop an almost flat direction. In this regime, confinement arises in a way similar to the 2 + 1 dimensional Polyakov mechanism and the monopoles and antimonopoles are effectively replaced by deconfined “bits” of a monopole loop.