Proving the Weak Gravity Conjecture in Perturbative String Theory, Part I: The Bosonic String

TL;DR

This paper provides a complete proof of the Weak Gravity Conjecture for perturbative bosonic string theories in spacetime dimensions six and above, linking black hole bounds to worldsheet calculations.

Contribution

It introduces a rigorous proof of the Weak Gravity Conjecture in bosonic string theory, establishing a sublattice version and addressing previous gaps in the literature.

Findings

Proof applies to D≥6 bosonic string theories

Establishes a strict sublattice form of the conjecture

Relates extremality bounds to worldsheet long-range forces

Abstract

We present a complete proof of the Weak Gravity Conjecture in any perturbative bosonic string theory in spacetime dimension $D\ge6$. Our proof works by relating the black hole extremality bound to long range forces, which are more easily calculated on the worldsheet, closing the gaps in partial arguments in the existing literature. We simultaneously establish a strict, sublattice form of the conjecture in the same class of theories. We close by discussing the scope and limitations of our analysis, along with possible extensions including an upcoming generalization of our work to the superstring.