Magnetic Monopole Molecules

We construct a variety of bound states of Dirac magnetic monopoles in product $U(1)$ gauge theories that make up a Dirac magnetic monopole with unit magnetic charge under the unbroken $U(1)$ gauge group. The size of the bound states is determined by the balance between the repulsive magnetic Coulomb force of the unbroken $U(1)$ gauge group and the attractive force from the tension of the magnetic flux tubes of the broken $U(1)$ gauge groups. These bound states are extensions of the configuration first studied in arXiv:1608.06951. We dub this type of configurations ``Magnetic Monopole Molecules'' (MMMs). Besides some illustrative examples of MMMs made of a small number of constituent Dirac magnetic monopoles, a method to combine smaller MMMs to construct larger MMMs is presented. Implications for the weak gravity conjecture are also discussed.