Taming the landscape of effective theories

We introduce a generalized notion of finiteness that provides structural principle for the set effective theories can be consistently coupled to quantum gravity. More concretely, we propose Tameness Conjecture states all valid are labelled by definable parameter space and must have scalar field spaces coupling functions using tame geometry built from an o-minimal structure. give brief introduction describe how it restricts sets, manifolds, functions. then collect evidence studying various arising string theory compactifications some recent advances in geometry. In particular, will exploit fact coset period mappings structure argue non-trivial tameness results higher-supersymmetric Calabi-Yau compactifications. As strongest over discrete space, discuss theorem stating locus self-dual flux vacua F-theory admits even if one allows any choice satisfying tadpole constraint. This result implies F-theory.