# A Solution to the Decompactification Problem in Chiral Heterotic Strings

## TL;DR

This paper proposes a method to resolve the decompactification problem in chiral heterotic string theories with large extra dimensions, ensuring gauge threshold corrections grow logarithmically rather than linearly with volume.

## Contribution

The authors identify the origin of the decompactification problem and demonstrate conditions under which gauge thresholds have only logarithmic volume dependence, with explicit string models illustrating the solution.

## Key findings

- Threshold corrections can be made to grow logarithmically with volume.
- Explicit string models show the decompactification problem can be avoided.
- Conditions for logarithmic volume dependence are established.

## Abstract

We present a solution to the decompactification problem of gauge thresholds in chiral heterotic string theories with two large extra dimensions, where supersymmetry is spontaneously broken by the Scherk-Schwarz mechanism. Whenever the Kaluza-Klein scale is much lower than the string scale, the infinite towers of heavy states contribute non-trivially to the renormalisation of gauge couplings, which typically grow linearly with the large volume of the internal space and invalidate perturbation theory. We trace the origin of the decompactification problem to properties of the six dimensional theory obtained in the infinite volume limit and show that thresholds may instead exhibit logarithmic volume dependence and we provide the conditions for this to occur. We illustrate this mechanism with explicit string constructions where the decompactification problem does not occur.