The Art of Networking: Networks of Trivalent 10d Heterotic Junctions

We initiate the study of networks of 10d string theories connected by junctions implied by the cobordism conjecture. Focusing on the recently constructed junction of the three 10d non-tachyonic heterotic theories, we generalize its $(0, 1)$ heterotic worldsheet description to construct arbitrary networks. For one-dimensional networks, we formulate their topology in terms of graph theory and provide a simple worldsheet realization for general graphs. We then extend our analysis to higher-dimensional networks, describing e.g. nucleation in a theory of bubbles of pairs of other theories. We also discuss compact configurations, which define a novel class of compactifications in which different sectors propagate on different compact spaces, in a way reminiscent of compactifications on quantum geometries like $S^1 \vee S^1$.