Threshhold Corrections in $K3\times T2$ Heterotic String Compactifications

TL;DR

This paper calculates one-loop threshold corrections to gauge and gravitational couplings in heterotic string compactifications on orbifolded K3 surfaces, providing explicit formulas for the prepotential and gravitational couplings in four-dimensional N=2 theories.

Contribution

It provides explicit calculations of threshold corrections and the one-loop prepotential for heterotic strings on Z_n orbifolds of K3, advancing understanding of moduli-dependent couplings.

Findings

Explicit formulas for threshold corrections to gauge couplings.

Derivation of the one-loop prepotential for vector multiplets.

Results applicable to Z_n orbifold compactifications.

Abstract

We consider compactifications of the heterotic string on $K3 \times T2$ so that the resulting theory in $d = 4$ space-time dimensions has $N = 2$ supersymmetry. The gravitational and gauge coupling constants of the low-energy effective theory receive threshold corrections from loops of super-heavy string states. We calculate these corrections for the case when the $K3$-surface is a ${\bf Z}_n$ orbifold of a four torus $T4$. The results are used to determine the one-loop prepotential ${\cal F}_0^{(1)}$ for the vector multiplets and the gravitational coupling ${\cal F}_1^{(1)}$.