Kahler Moduli Stabilization and the Propagation of Decidability

TL;DR

This paper shows that certain Diophantine equations in string theory are decidable and that this decidability can spread through networks of string vacua, aiding in Kahler moduli stabilization.

Contribution

It demonstrates the propagation of decidability in Diophantine equations within string theory networks, enhancing understanding of moduli stabilization.

Findings

Decidability propagates through networks of geometries.

Most divisor classes appear in at least one solution.

Improves prospects for Kahler moduli stabilization.

Abstract

Diophantine equations are in general undecidable, yet appear readily in string theory. We demonstrate that numerous classes of Diophantine equations arising in string theory are decidable and propose that decidability may propagate through networks of string vacua due to additional structure in the theory. Diophantine equations arising in index computations relevant for D3-instanton corrections to the superpotential exhibit propagation of decidability, with new and existing solutions propagating through networks of geometries related by topological transitions. In the geometries we consider, most divisor classes appear in at least one solution, significantly improving prospects for Kahler moduli stabilization across large ensembles of string compactifications.