Strong Coupling Expansion Of Calabi-Yau Compactification

TL;DR

This paper explores the strong coupling limit of heterotic string compactification on Calabi-Yau manifolds, analyzing supersymmetry equations and the bounds on Newton's constant to understand when strong coupling arises.

Contribution

It provides a first-order expansion of supersymmetry equations near the strong coupling limit, verifying the consistency of the eleven-dimensional description and estimating bounds on Newton's constant.

Findings

Supersymmetry equations are consistent at first order near the limit.

Strong coupling occurs if Newton's constant is made too small.

Estimated lower bound on Newton's constant is close to its actual value.

Abstract

In a certain strong coupling limit, compactification of the $E_8\times E_8$ heterotic string on a Calabi-Yau manifold $X$ can be described by an eleven-dimensional theory compactified on $X\times \S^1/\Z_2$. In this limit, the usual relations among low energy gauge couplings hold, but the usual (problematic) prediction for Newton's constant does not. In this paper, the equations for unbroken supersymmetry are expanded to the first non-trivial order, near this limit, verifying the consistency of the description and showing how, in some cases, if one tries to make Newton's constant too small, strong coupling develops in one of the two $E_8$'s. The lower bound on Newton's constant (beyond which strong coupling develops) is estimated and is relatively close to the actual value.