Demystifying the Emergence Proposal

TL;DR

This paper explores the Emergence Proposal in type IIA string theory, demonstrating that in certain limits, couplings can be exactly derived from infinite towers of states, linking to mirror symmetry and Gopakumar-Vafa invariants.

Contribution

It provides an exact formulation of emergence in four-dimensional N=2 string vacua, connecting couplings to infinite towers of states and geometric invariants.

Findings

Couplings can be exactly computed in asymptotic limits.

Emergent theories include infinite towers of states up to the species scale.

Decompactification limits relate to Gopakumar-Vafa invariants and tensionless branes.

Abstract

We revisit the Emergence Proposal in the vector multiplet moduli space of type IIA N=2 supersymmetric string vacua in four dimensions, for which the string tree-level prepotential and the string one-loop correction are exactly known via mirror symmetry. We argue that there exists an exact notion of emergence, according to which these four-dimensional couplings can be computed exactly in any asymptotic limit in field space. In such limits, a perturbative quantum gravity theory emerges, whose fundamental degrees of freedom include all complete infinite towers of states with typical mass scale not larger than the species scale. For a decompactification limit, this picture is closely related to and in fact motivated by the computation of Gopakumar-Vafa invariants. In addition, in the same limit our results suggest that the emergent theory will also contain asymptotically tensionless wrapped NS5-branes.