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The Swampland Distance Conjecture proposes that approaching infinitedistances in field space an infinite tower of states becomes exponentiallylight. We study this conjecture for the complex structure moduli space ofCalabi-Yau manifolds. In this context, we uncover significant structure withinthe proposal by showing that there is a rich spectrum of different infinitedistance loci that can be classified by certain topological data derived froman associated discrete symmetry. We show how this data also determines therules for how the different infinite distance loci can intersect and form aninfinite distance network. We study the properties of the intersections indetail and, in particular, propose an identification of the infinite tower ofstates near such intersections in terms of what we term charge orbits. Theseorbits have the property that they are not completely local, but depend on datawithin a finite patch around the intersection, thereby forming an initial steptowards understanding global aspects of the distance conjecture in fieldspaces. Our results follow from a deep mathematical structure captured by theso-called orbit theorems, which gives a handle on singularities in the modulispace through mixed Hodge structures, and is related to a local notion ofmirror symmetry thereby allowing us to apply it also to the large volumesetting. These theorems are general and apply far beyond Calabi-Yau modulispaces, leading us to propose that similarly the infinite distance structureswe uncover are also more general.

Infinite Distance Networks in Field Space and Charge Orbits