Superstring Threshold Corrections to Yukawa Couplings

TL;DR

This work presents a general, string-based method to compute one-loop corrections to the Kähler metric and physical Yukawa couplings in heterotic compactifications, yielding a direct string-theory determination of the Green-Schwarz term. It shows how infrared divergences reproduce field-theoretic anomalous dimensions while finite parts produce moduli-dependent threshold corrections that set unification-scale Yukawa boundary conditions. Through explicit analysis of symmetric orbifold models, it reveals that special geometry is typically violated beyond tree level and identifies how untwisted and twisted sectors contribute to moduli and matter metrics differently. The results provide a concrete framework for connecting worldsheet computations to low-energy couplings, with implications for moduli stabilization, coupling unification, and phenomenology in heterotic string vacua.

Abstract

A general method of computing string corrections to the Kähler metric and Yukawa couplings is developed at the one-loop level for a general compactification of the heterotic superstring theory. It also provides a direct determination of the so-called Green-Schwarz term. The matter metric has an infrared divergent part which reproduces the field-theoretical anomalous dimensions, and a moduli-dependent part which gives rise to threshold corrections in the physical Yukawa couplings. Explicit expressions are derived for symmetric orbifold compactifications.