Geometry, topology, and gravitation synthesized by cosmic strings

In the context of static cosmic strings, the Einstein equations coupled to the Abelian Higgs model and the gauged σ-model reduce into a single equation, which directly relates the Gauss curvature of a Riemann surface hosting nontrivial geometry and gravitation to the energy density of the coupled matter-gauge sector. This equation gives rise to an equivalence relation between the topology of the Riemann surface and the topology of the complex line bundle which hosts and is determined by the physical in- teractions of the matter-gauge sector. The existence of solutions realizing a prescribed distribution of cosmic strings resembles the classical prescribed Gauss curvature problem.