On the particle picture of Emergence

The Emergence Proposal is the idea that all kinetic terms for fields in quantum gravity are emergent in the infrared from integrating out towers of states. It predicts that in a supersymmetric string theory context, the tree-level prepotential terms can be recovered precisely by integrating out a tower of non-perturbative states. In this note we present a new perspective, and associated quantitative evidence, for this proposal. We argue that the tree-level kinetic terms arise from integrating out the ultraviolet physics of each of the states in the tower. This ultraviolet physics is associated to extended objects, and cannot be captured by a standard particle Schwinger integral. Instead, we argue that it should be captured by a Schwinger-like integral where the proper time is analytically continued, and a contour is taken around the origin. This maps to certain integral representations for the moduli space periods, and indeed one recovers the tree-level prepotential exactly. This interpretation suggests that the ultraviolet physics which gives the leading contribution to the prepotential is localised on point intersections of the extended objects. We also argue that over special loci in moduli space there can exist a particle picture of the states, and an associated simple particle Schwinger integral, which leads to the full tree-level prepotential. These are loci with special degenerations, such as the singular limit of the resolved conifold.