Moduli Corrections to Gauge and Gravitational Couplings in four dimensional Superstrings

TL;DR

This paper derives general formulas for one-loop moduli-dependent corrections to gauge and gravitational couplings in heterotic string vacua, using their relation to CP-odd couplings and four-point functions in N=2 superconformal theories.

Contribution

It provides a unified approach to compute moduli corrections in both (2,2) and (2,0) heterotic string models, including symmetric orbifolds.

Findings

Derived explicit expressions for moduli corrections.

Connected corrections to CP-odd couplings and four-point functions.

Analyzed corrections in symmetric orbifold models.

Abstract

We study one-loop, moduli-dependent corrections to gauge and gravitational couplings in supersymmetric vacua of the heterotic string. By exploiting their relation to the integrability condition for the associated CP-odd couplings, we derive general expressions for them, both for $(2,2)$ and $(2,0)$ models, in terms of tree level four-point functions in the internal $N=2$ superconformal theory. The $(2,2)$ case, in particular symmetric orbifolds, is discussed in detail.