Moduli Corrections to Gauge and Gravitational Couplings in four dimensional Superstrings

TL;DR

The paper tackles the problem of determining moduli-dependent one-loop corrections to gauge and gravitational couplings in heterotic four-dimensional vacua. Its approach centers on expressing threshold corrections through the violation of the integrability condition for CP-odd Theta-angles and relating them to tree-level four-point amplitudes in the internal $N=2$ superconformal theory, covering both $(2,2)$ and $(2,0)$ models. It provides explicit formulas for the Theta-terms and their gravitational counterparts, with detailed results for $(2,2)$ orbifolds that distinguish untwisted, twisted, and blowing-up moduli, and it demonstrates consistency with effective field theory anomalous graphs. The work clarifies how threshold corrections are governed by worldsheet CFT data and moduli-space geometry, highlighting potential discontinuities at special loci and proposing infrared regularization as a path to continuous, duality-invariant results, with implications for moduli stabilization and supersymmetry breaking analyses.

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.