Speaker
Description
For non-compact, locally symmetric moduli spaces ${\cal M}$, the set of geodesics and the geometry of the boundary can be completely characterised using group-theory notions. In particular, geodesics that reach infinite distance (which are a set of measure zero) are associated to rational parabolic subgroups of the isometry group $G$. Under the mild assumptions that ${\cal M}$ has finite volume and that the spectrum of states is complete, we use this relation to prove the swampland distance conjecture for all such spaces ${\cal M}$. Furthermore, the lattice of states forms a representation of $G$, and we show that the convex hull encoding the exponential rate of the leading tower of states becoming light is simply the convex hull of the weights of the representation. For an irreducible representation, this is the Weyl polytope built from the highest weight vector. We classify all such polytopes that are consistent with the emergent string and sharpened distance conjecture, and find that there are only finitely many classes, which we list. For each group only one representation for particles is allowed, and the space-time dimension can only have a fixed value.
