Dirac string

In physics, a Dirac string is a fictitious one-dimensional curve in space, stretched from a magnetic monopole - also called the Dirac monopole - to infinity. The gauge potential cannot be defined on the Dirac string, but it is defined everywhere else. The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of $2\pi$.

The quantization forced by the Dirac string can be understood in terms of the cohomology of the fibre bundle representing the gauge fields over the base manifold of space-time. The magentic charges of a gauge field theory can be understood to be the group generators of the cohomology group $H_{1}(M)$ for the fiber bundle M.