The Emergence Proposal in Quantum Gravity and the Species Scale

In the Emergence Proposal in QG it is conjectured that all light-particle kinetic terms are absent in the fundamental UV theory and are generated by quantum corrections in the IR. It has been argued that this proposal may provide for some microscopic understanding of the WGC and SDC. In the present paper we take the first steps towards a general systematic study of emergence in the context of string theory. We emphasize the crucial role the \textit{species scale} plays in any EFT coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of emergence and we show how kinetic terms for moduli, $p$-forms and fermions may be generated. One-loop computations play an important role in emergence and we present detailed computations in $d$ spacetime dimensions for the relevant wave-function renormalizations. We extend and check the Emergence Proposal in a number string theory vacua, including 4d $\mathcal{N}=2$ theories arising from type IIA on a CY$_3$, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the Emergence picture. Higher dimensional examples are also discussed, including 6d and 7d (supersymmetric) models arising from F-/M-theory on an elliptic CY$_3$ or a $K3$ surface, respectively. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from emergence, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini. Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in QG as an intrinsic IR phenomenon.