UV/IR relations from the worldsheet

TL;DR

This paper establishes universal relations in string theory linking low-energy parameters to higher-derivative terms, supporting emergent string conjectures and swampland principles through one-loop string perturbation analysis.

Contribution

It derives parametric relations from worldsheet invariance that connect UV and IR physics, strengthening the emergent string conjecture and relating to swampland ideas.

Findings

Relations hold at one-loop, independent of the low-energy phase.

Results support the magnetic weak-gravity conjecture.

Parametric inequalities align with holographic bounds.

Abstract

We derive universal scaling relations for the low-energy effective action of string theory, connecting the vacuum energy and gauge couplings to higher-derivative Wilson coefficients. At one-loop in string perturbation theory, these generic parametric relations follow from modular and conformal invariance of the worldsheet, independently of the specific low-energy phase of the theory, and they become non-trivial in species limits. As a result, we substantially strengthen our previous case for the emergent string conjecture and connect UV/IR mixing to swampland principles. We argue that our results persist to higher loops, hinting at a pathway to study strong couplings using dualities. Further accounting for open-string contributions, if any, our results lead to parametric inequalities which reproduce holographic bounds and support the magnetic weak-gravity conjecture and the dark dimension scenario.