Taxonomy of infinite distance limits

A bstract The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors ( $$ -\overrightarrow{\nabla} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:mover> <mml:mo>∇</mml:mo> <mml:mo>→</mml:mo> </mml:mover> </mml:math> log m ) of the light towers and the analogous vector ( $$ -\overrightarrow{\nabla} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:mover> <mml:mo>∇</mml:mo> <mml:mo>→</mml:mo> </mml:mover> </mml:math> log Λ QG ) of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints.