Moduli Dependence of One--Loop Gauge Couplings in (0,2) Compactifications
P. Mayr, S. Stieberger
TL;DR
The paper investigates how the moduli of a four-dimensional heterotic (0,2) orbifold control the one-loop gauge couplings, focusing on Wilson-line moduli. It develops a framework in which threshold corrections are represented as automorphic functions on an auxiliary Riemann surface, expressing the three-moduli dependence ($T$, $U$, $B$, $C$) through genus-two Siegel modular forms and genus-two theta representations. Explicit formulas are derived for three threshold classes corresponding to different singularity structures, and a genus-two degeneration to genus-one limits is shown to reproduce known results and enable a systematic $q_T$-expansion. The work highlights a rich interplay between duality symmetries, automorphic forms, and two-dimensional interpretations, with potential implications for gauge-coupling unification and S-duality in related theories.
Abstract
We derive the moduli dependence of the one--loop gauge couplings for non--vanishing gauge background fields in a four--dimensional heterotic (0,2) string compactification. Remarkably, these functions turn out to have a representation as modular functions on an auxiliary Riemann surface on appropriate truncations of the full moduli space. In particular, a certain kind of one--loop functions is given by the free energy of two--dimensional solitons on this surface.