Tameness, Strings, and the Distance Conjecture

A bstract The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching distance point in field space. We argue the inherent path-dependence this statement can be addressed combining with recent Tameness Conjecture. latter asserts effective theories are described by tame geometry and implements strong finiteness constraints on coupling functions spaces. By exploiting these tameness we region near admits a decomposition into finitely many sectors which path-independent statements for associated towers established. then introduce more constrained class at most polynomial asymptotic growth they suffice to describe known string theory actions. Remarkably, multi-field dependence such reconstructed one-dimensional linear test paths each sector boundary. In four-dimensional theories, traced out as discrete set cosmic solutions. This indicates solutions serve powerful tool study near-boundary space any theory. To illustrate general observations discuss central role Calabi-Yau compactifications Type IIB