Threshold Corrections and Symmetry Enhancement in String Compactifications

TL;DR

This paper computes threshold functions in Abelian orbifold compactifications, revealing how moduli and Wilson lines influence gauge and gravitational couplings, especially at points where extra massless states emerge due to symmetry enhancement.

Contribution

It provides a detailed derivation of moduli-dependent threshold functions incorporating Wilson lines and analyzes the emergence of massless states at critical points in orbifold moduli spaces.

Findings

Threshold functions depend on continuous Wilson line moduli.

Logarithmic singularities occur at critical moduli points with extra massless states.

These singularities impact loop corrections to gauge and gravitational couplings.

Abstract

We present the computation of threshold functions for Abelian orbifold compactifications. Specifically, starting from the massive, moduli-dependent string spectrum after compactification, we derive the threshold functions as target space duality invariant free energies (sum over massive string states). In particular we work out the dependence on the continuous Wilson line moduli fields. In addition we concentrate on the physically interesting effect that at certain critical points in the orbifold moduli spaces additional massless states appear in the string spectrum leading to logarithmic singularities in the threshold functions. We discuss this effect for the gauge coupling threshold corrections; here the appearance of additional massless states is directly related to the Higgs effect in string theory. In addition the singularities in the threshold functions are relevant for the loop corrections to the gravitational coupling constants.